Method and apparatus for low density parity check channel coding in wireless communication system

ABSTRACT

Embodiments of this application disclose provides a low density parity check (LDPC) channel encoding method for use in a wireless communications system. A communication device encodes an input bit sequence by using a LDPC matrix, to obtain an encoded bit sequence for transmission. The LDPC matrix is obtained based on a lifting factor Z and a base matrix. Embodiments of the application provide eight particular designs of the base matrix. The encoding method provided in the embodiments of the application can be used in various communications systems including the fifth generation (5G) telecommunication systems, and can support various encoding requirements for information bit sequences with different code lengths.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of International Application No.PCT/CN2018/082851, filed on Apr. 12, 2018. The International Applicationclaims priority to Chinese Patent Application No. 201710503056.2, filedon Jun. 27, 2017 and Chinese Patent Application No. 201710572364.0,filed on Jul. 13, 2017. The afore-mentioned patent applications arehereby incorporated by reference in their entireties.

TECHNICAL FIELD

Embodiments of the present application relate to the communicationsfield, and in particular, to an information processing method and acommunication apparatus.

BACKGROUND

Information transmitted in a wireless communication channel is usuallyencoded by a channel coding scheme such as Turbo code, Polar code andlow density parity check (LDPC) code. LDPC code is a type of linearblock code characterized by a sparse check matrix (referred to as a LDPCmatrix), and has a flexible structure and low decoding complexity.Because a partially parallel iterative decoding algorithm can be used indecoding an LDPC coded codeword, the LDPC code has a higher throughputthan a conventional Turbo code. The LDPC code may be used as an errorcorrection code in a communication system, so as to improve reliabilityand power utilization in channel-based transmission. The LDPC code mayalso be widely used in spatial communications, optical fibercommunications, personal communication systems, asymmetrical digitalsubscriber loop (ADSL), magnetic recording devices, and the like.Currently, the LDPC code has been considered as one of channel codingschemes in the fifth generation (5G) mobile communication systems.

In actual applications, LDPC matrices having different specialstructures may be used. An LDPC matrix H, having a special structure,may be obtained by expanding (also called lifting) an LDPC base matrixhaving a quasi cycle (QC) structure (H is referred to as a QC-LDPCmatrix). A coding scheme using QC-LDPC matrices is suitable for hardwarewith a high degree of parallelism, and provides a higher throughput. TheQC-LDPC matrix may be designed to be suitable for channel coding.

SUMMARY

Embodiments of the present application provide an information processingmethod, and a communication apparatus and system, so as to supportencoding and decoding of information bit sequences with a plurality oflengths.

According to a first aspect, an encoding method and an encoder areprovided. The encoder encodes an input sequence by using a low densityparity check (LDPC) matrix.

According to a second aspect, a decoding method and a decoder areprovided. The decoder decodes an input sequence by using an LDPC matrix.

In a first implementation of the first aspect or the second aspect, theLDPC matrix is obtained based on a lifting factor Z and a base matrix.

The base matrix of a base graph includes one of the following:

1. the base matrix includes row 0 to row 6, column 0 to column 16 of oneof matrices shown in FIG. 3b -1 to 3 b-8, or

2. the base matrix includes row 0 to row 6, some columns of column 0 tocolumn 16 in one of matrices shown in FIG. 3b -1 to 3 b-8, or

3. the base matrix is a matrix obtained by performing row/columntransformation on row 0 to row 6 column 0 to column 16 in one ofmatrices shown in FIG. 3b -1 to 3 b-8, or

4. the base matrix is a matrix obtained by performing row/columntransformation on row 0 to row 6, some columns of column 0 to column 16in one of matrices shown in FIGS. 3b -1 to 3 b-8.

To support different code block lengths, different lifting factors Z areneeded for an LDPC code. Based on the foregoing implementations, basematrices corresponding to different lifting factors Z are used based onthe different lifting factors Z. In some implementations, Z=a×2^(j),where 0≤j<7, and a ∈{2, 3, 5, 7, 9, 11, 13, 15}.

Further, based on the foregoing implementations, the LDPC matrix may beobtained based on a lifting factor Z and a matrix Hs that is obtained byoffsetting the foregoing base matrix. Alternatively, the LDPC matrix maybe obtained based on a lifting factor Z and a matrix that is obtained byperforming row/column transformation on a matrix Hs, and Hs is obtainedby offsetting the foregoing base matrix. The offsetting the foregoingbase matrix may be increasing or decreasing a shift value greater thanor equal to 0 in one or more columns by an offset.

The base graph and the base matrix of the LDPC matrix in the foregoingimplementations can satisfy a performance requirement of code blocks ofa plurality of block lengths.

The lifting factor Z may be determined by the encoder or the decoderbased on a length K of the input sequence, or may be determined byanother device and provided to the encoder or the decoder as an inputparameter. Optionally, the LDPC matrix may be obtained based on theobtained lifting factor Z and a base matrix corresponding to the liftingfactor Z.

In a second implementation of the first aspect or the second aspect, theLDPC matrix is obtained based on the lifting factor Z and parameter(s)of the LDPC matrix.

The parameters of the LDPC matrix may include a row index, a columnindex of a column in which a non-zero-element is located, and a shiftvalue of the non-zero-element. The parameters are stored in manners likerow 0 to row 6 in one of Table 2 and Table 3b-1 to Table 3b-8. Theparameters of the LDPC matrix may further include a row weight.Locations of non-zero-elements in columns are in a one-to-onecorrespondence with shift values of the non-zero-elements.

For a communication device at a transmitting side, the encoding an inputsequence by using an LDPC matrix may include: encoding the inputsequence by using an LDPC matrix corresponding to the lifting factor Z;or encoding an input sequence by using a matrix that is obtained byperforming row/column transformation on an LDPC matrix corresponding tothe lifting factor Z. The row/column transformation in this applicationmeans row transformation, column transformation, or row transformationand column transformation.

For a communication device at a receive side, the decoding an inputsequence by using an LDPC matrix may include: decoding the inputsequence by using an LDPC matrix corresponding to the lifting factor Z;or decoding the input sequence by using a matrix that is obtained byperforming row/column transformation on an LDPC matrix corresponding tothe lifting factor Z. The row/column transformation in this applicationmeans row transformation, column transformation, or row transformationand column transformation.

In a possible implementation, an LDPC matrix may be stored, and the LDPCmatrix is used to encode the input sequence, or an LDPC matrix that canbe used for encoding is obtained by performing transformation(row/column transformation) or lifting based on the LDPC matrix.

In another possible implementation, a parameter or parameters may bestored, and an LDPC matrix used for encoding or decoding may be obtainedbased on the parameter, so that the input sequence can be encoded ordecoded based on the LDPC matrix. The parameter or parameters include atleast one of the following: a base graph, a base matrix, a transformedmatrix obtained by performing row/column transformation on a base graphor a base matrix, a lifting matrix based on a base graph or a basematrix, a shift value of a non-zero-element in a base matrix, or anyparameter used to obtain the LDPC matrix.

In still another possible implementation, the base matrix of the LDPCmatrix may be stored in a memory.

In yet another possible implementation, the base graph of the LDPCmatrix may be stored in a memory, and the shift value of thenon-zero-element in the base matrix of the LDPC matrix may be stored inthe memory.

In still yet another possible implementation, the parameter of the LDPCmatrix is stored in a memory in manners like Table 2 or Table 3b-1 toTable 3b-8, or some element groups of the parameter may be stored.

Based on the foregoing possible implementations, in a possible design,at least one of a base graph and a base matrix used for LDPC encoding ordecoding is obtained by performing row transformation, or columntransformation, or row transformation and column transformation on atleast one of the base graph and the base matrix of the LDPC matrix.

According to a third aspect, a communication apparatus is provided. Thecommunication apparatus may include software modules and/or hardwarecomponents configured to perform the foregoing method designs.

In a possible design, the communication apparatus provided in the thirdaspect includes a processor and a transceiver component. The processorand the transceiver component may be configured to perform any one ofthe possible implementations of the encoding method or the decodingmethod. The communication apparatus may be a terminal, a base station,or another network device, and the transceiver component of thecommunication apparatus may be a transceiver. The communicationapparatus may be a baseband chip or a baseband board, and thetransceiver component of the communication apparatus may be aninput/output circuit of the baseband chip or the baseband board, and isconfigured to receive/send an input/output signal. Optionally, thecommunication apparatus may further include a memory, configured tostore data and/or an instruction.

In an implementation, the processor may include the encoder according tothe first aspect and a determining unit. The determining unit isconfigured to determine a lifting factor Z required to encode an inputsequence. The encoder is configured to encode the input sequence byusing an LDPC matrix corresponding to the lifting factor Z.

In another implementation, the processor may include the decoderaccording to the second aspect and an obtaining unit. The obtaining unitis configured to obtain a soft value of an LDPC code and a liftingfactor Z. The decoder is configured to decode the soft value of the LDPCcode based on a base matrix H_(B) corresponding to the lifting factor Z,to obtain an information bit sequence.

According to a fourth aspect, a communication apparatus is provided. Thecommunication apparatus includes one or more processors. In a possibledesign, the one or more processors configured to perform any one of thepossible implementations of the encoder according to the first aspect.In another possible design, the encoder according to the first aspectmay be a part of the processor. In addition to the functions of theencoder according to the first aspect, the processor can furtherimplement other functions. In a possible design, the one or moreprocessors can implement functions of the decoder according to thesecond aspect. In another possible design, the decoder according to thesecond aspect may be a part of the processor.

Optionally, the communication apparatus may further include atransceiver and an antenna.

Optionally, the communication apparatus may further include a componentfor transport block cyclic redundancy check (CRC), a component for codeblock segmentation and CRC check, an interleaver for interleaving, amodulator for modulation processing, or the like. In a possible design,functions of these components may be implemented by using the one ormore processors.

Optionally, the communication apparatus may further include ademodulator for a demodulation operation, a deinterleaver fordeinterleaving, a component for rate de-matching, or the like. Functionsof these devices may be implemented by using the one or more processors.

According to a fifth aspect, an embodiment of the present applicationprovides a communication system. The system includes the communicationapparatus according to the third aspect.

According to a sixth aspect, an embodiment of the present applicationprovides a communication system. The system includes one or morecommunication apparatuses according to the fourth aspect.

According to still another aspect, an embodiment of the presentapplication provides a computer storage medium. The computer storagemedium stores a program, and when the program is run, a computer iscaused to perform the methods described in the foregoing aspects.

Yet another aspect of this application provides a computer programproduct including an instruction, when the instruction is run on acomputer, the computer is caused to perform the methods according to theforegoing aspects.

According to the information processing method, the apparatus, thecommunication device, and the communication system in the embodiments ofthe present application, flexible code length and code rate requirementsof a system can be met in terms of encoding performance and an errorfloor.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 shows examples of a base graph, a base matrix, and circularpermutation matrices that are used in LDPC code;

FIG. 2 is a schematic structural diagram of a base graph and examples ofa core part of the base graph;

FIG. 3a is a base graph according to an embodiment of the presentapplication;

FIGS. 3b -1 to 3 b-8 are base matrices according to embodiments of thepresent application;

FIG. 4 is a performance diagram provided by an embodiment of the presentapplication;

FIG. 5 is a flowchart of an information processing procedure accordingto an embodiment of the present application;

FIG. 6 is a flowchart of an information processing procedure accordingto an embodiment of the present application;

FIG. 7 is a simplified block diagram of a communication apparatusaccording to an embodiment of the present application; and

FIG. 8 is a block diagram of a communication system according to anembodiment of the present application.

DETAILED DESCRIPTION OF EMBODIMENTS

For ease of understanding, the following describes some terms used inthis application.

In this application, terms “network” and “system” are ofteninterchangeably used, “apparatus” and “device” are often interchangeablyused, and “information” and “data” are also often interchangeably used.Means of these terms are conventionally understood. A “communicationapparatus” may refer to a chip (for example, a baseband chip, a digitalsignal processing chip, or a general-purpose chip), a terminal, a basestation, or other network devices. The article “a” or “an” is intendedto indicate one or more.

A terminal is a device having communication functions. A terminal may bea handheld device, an in-vehicle device, a wearable device, or otherkinds of devices that have wireless communication functions. A terminalmay be called by different names in different networks, such as userequipment, mobile station, subscriber unit, station, cellular phone,personal digital assistant, wireless modem, wireless communicationdevice, handheld device, laptop computer, cordless telephone set, orwireless local loop station. For ease of description, these devices arecollectively referred to as a terminal in this application.

A base station or a base station device is a device deployed in a radioaccess network to provide wireless communication functions. The basestation may be called by different names in different wireless accesssystems. For example, a base station in a Universal MobileTelecommunications System (UMTS) network is referred to as a NodeB. Abase station in a long term evolution (LTE) network is referred to as anevolved NodeB (eNB or eNodeB). A base station in a new radio (NR)network is referred to as a transmission reception point (TRP) or a nextgeneration NodeB (gNB). Base stations in other networks may be called byother names. This is not limited in the present application.

The technical solutions in the embodiments of the present applicationare described below with reference to the accompanying drawings.

An LDPC code can be defined by a parity check matrix H. In animplementation, the parity check matrix H for LDPC code, also referredto as a LDPC matrix, is represented by a matrix called a base graph. Anexample of the base graph 10 a is shown in FIG. 1. Each element in thebase graph 10 a represents a Z×Z spreading (lifting) matrix. Z is apositive integer, and is referred to as a lifting factor. Z may also bereferred to as a lifting size or the like. The base graph is used toindicate locations of zero-elements and non-zero-elements. Eachnon-zero-element in the base graph 10 a corresponds to a shift value, asshown in FIG. 1, matrix 10 b. The parity check matrix H for the LDPCcode may be obtained based on the base graph and shift values. Usually,a base graph includes m×n matrix elements (also called entries), and isrepresented by a matrix of m rows and n columns. A value of each matrixelement is either 0 or 1. An element whose value is 0 is called azero-element, which corresponds to a Z column×Z row all-zero matrix. Anelement whose value is 1 is called a non-zero-element, which correspondsto a Z column×Z row circular permutation matrix. In other words, eachelement of the base graph represents either an all zero matrix or acircular permutation matrix. In the base graph example 10a shown in FIG.1, m=7 and n=17, and the base graph 10 a has a QC structure.

It should be noted that, throughout this application, row indexes andcolumn indexes of base graphs and base matrices are numbered startingfrom 0, and this is merely for ease of description. For example, columnindex 0 represents a first column in a base graph or a base matrix,column index 1 represents a second column in the base graph or the basematrix, row index 0 represents a first row in the base graph or the basematrix, row index 1 represents a second row in the base graph or thebase matrix, and so on.

It should be understood that the rows and the columns of the base graphor the base matrix may be numbered by other manners, and the presentapplication is not limited by any particular manner of numbering.

A base matrix of m rows and n columns (which is sometimes referred to asa parity check matrix (PCM)) may be specifically defined. Matrix 10 b inFIG. 1 is a particular example of the base matrix. Elements in the basematrix 10 b are in a one-to-one correspondence with elements in the basegraph 10 a. A zero-element in the base graph 10 a has a same position inthe base matrix 10 b. In the base matrix 10 b, a zero-element isrepresented by −1 or “null”. A non-zero-element in row i and column j,whose value is 1 in the base graph 10 a, corresponds to a non-zeroelement at a same position in the base matrix 10 b. The non-zero-elementis represented by a value V_(i,j). V_(i,j) may be defined by a system,may be predefined, or may be obtained based on a shift value P_(i,j) anda lifting factor Z. P_(i,j) is a shift value corresponding to apredetermined or a particular lifting factor Z. P_(i,j) may be obtainedbased on Z and V_(i,j). In an implementation, P_(i,j) and V_(i,j)satisfy the following relationship:

P _(i,j)=mod(V _(i,j) ,Z)

where i and j represent a row index and a column index of the non-zeroelement, and indicate a location of the element in the base matrix.

In the embodiments of this application, sometimes the base matrix isalso referred to as a shift matrix of the base graph. The base matrixmay be obtained according to the base graph and the shift value. If anelement in row i and column j of the base graph has a value 1, and ashift value of the element is P_(i,j), where P_(i,j) is an integergreater than or equal to 0, it indicates that the element can bereplaced by a Z×Z circular permutation matrix corresponding to P_(i,j).The circular permutation matrix may also be referred to as a shiftmatrix. The circular permutation matrix may be obtained by circularlyshifting a Z×Z identity matrix to the right or to the left for P_(IS)times. In an implementation,

P _(i,j)=mod(V _(i,j) ,Z)

where V_(i,j) is a value in the base matrix, that is corresponding to anon-zero-element in the base graph.

Sometimes, V_(i,j) may also be referred to as a shift value, a cyclicshift value, or a shift coefficient. V_(i,j) may be, for example, ashift value corresponding to a maximum lifting factor Z_(max). Z_(max)is a maximum value in a value set of Z. If a value of an element in rowi and column j in the base graph is 0, the element may be replaced witha Z×Z all zero matrix. If a value of an element in row i and column j inthe base graph is 1, the element may be replaced with a Z×Z circularpermutation matrix having the shift value of P_(i,j). In this way, aparity check matrix H for the LDPC code is obtained.

Z is a positive integer, and may be referred to as a lifting factor, alifting size, or the like. Z may be determined based on a code blocksize and an information data size that are supported by a system. It canbe seen that for a base graph of m rows×n columns, a size of the paritycheck matrix H for the LDPC code is (m×Z) rows×(n×Z) columns. Forexample, if the lifting factor Z is 4, each zero-element is replacedwith an all zero matrix of size 4×4 (see 11 a of FIG. 1). If P_(2,3)=2,a non-zero-element in row 2 and column 3 of the base matrix is replacedwith a 4×4 circular permutation matrix 11 d of FIG. 1. The matrix 11 dis obtained by circularly shifting a 4×4 identity matrix 11 b rightwardtwice. If P_(2,4)=0, a non-zero-element in row 2 and column 4 isreplaced with the identity matrix 11 b. It should be noted that, thisexample is merely for illustration, and is not intended to impose alimitation.

Value of P_(i,j) may depend on the lifting factor Z. For an element of 1(a non-zero element) in row i and column j of the base graph, P_(i,j)may be different for different lifting factors Z. For example, for avalue of 1 in row 1 and column 3 in the base graph 10 a, a correspondingshift value V_(i,j) in row 1 and column 3 in the base matrix 10 b is 27.The value of P_(i,j) may be obtained according to P_(i,j)=mod(V_(i,j),Z). In this way, an element in row 1 and column 3 can be replaced with acircular permutation matrix that is obtained by circularly shifting anidentity matrix of size Z×Z rightward or leftward for P_(i,j) times.

Usually, the base graph or the base matrix for the LDPC code may furtherinclude p columns of built-in puncture column, where p may be an integerfrom 0 to 2. These columns may be used in encoding, but the encodedsystem bits corresponding to the built-in puncture columns are not sent.In this case, a code rate of the base matrix for the LDPC code satisfiesR=(n−m)/(n−p). Using the base graph 10 a as an example, if there are twobuilt-in puncture columns, the code rate is (17-7)/(17-2)=0.667, whichis approximately ⅔.

As mentioned above, an LDPC code used in a wireless communication systemis a QC-LDPC code. A parity bit part of the QC-LDPC code has abi-diagonal structure or a raptor-like structure. This can simplifyencoding and support incremental redundancy hybrid repeat. A decoder forthe QC-LDPC code usually uses a QC-LDPC shift network (QSN), a Banyannetwork, or a Benes network, to cyclical shift information.

As shown in FIG. 2, a base graph 200 for the QC-LDPC code, which has araptor-like structure, is a matrix of m rows and n columns. The basegraph 200 may include five submatrices A, B, C, D, and E. A weight of arow or a column of the matrix is determined by quantity ofnon-zero-elements in the row or the column. A weight of a row (rowweight) means a quantity of non-zero-elements in a row, and a weight ofa column (column weight) means a quantity of non-zero-elements in acolumn. The following is shown in base graph 200 of FIG. 2:

The submatrix A is a matrix of m_(A) rows and n_(A) columns, and a sizeof the submatrix A is m_(A)×n_(A). Each column corresponds to Z systembits in the LDPC code, and a system bit is sometimes referred to as aninformation bit.

The submatrix B is a matrix of m_(A) rows and m_(A) columns, and a sizeof the submatrix B is m_(A)×m_(A). Each column corresponds to Z paritybits in the LDPC code. Further shown in 20 a of FIG. 2, the submatrix Bincludes a submatrix B′ having a bi-diagonal structure and a matrixcolumn whose column weight is 3 (weight-3 column for short). Theweight-3 column may be located at the left side of the submatrix B′. Thesubmatrix B may further include one or more matrix columns whose columnweights are 1 (weight-1 column for short). 20 b and 20 c of FIG. 2 areexamples of possible locations of the weight-1 columns.

Usually, a matrix generated based on the submatrices A and B may bereferred to as a core matrix, which may be used to support highcode-rate encoding.

The submatrix C is an all zero matrix, and a size of the submatrix C ism_(A)×m_(D).

The submatrix E is an identity matrix, and a size of the submatrix E ism_(D)×m_(D), where m_(D)=m-m_(A).

A size of the submatrix D is m_(D)×(n_(A)+m_(A)), and may usually beused to generate low code-rate parity bits.

Because the submatrices C and E have relatively definite structures,structures of the three submatrices A, B, and D are some of the factorsaffecting encoding/decoding performance of the LDPC code.

The foregoing describes the structure of the base graph/the base matrixfrom a perspective of principles. The division of the submatrices A, B,C, D, and E is merely to facilitate understanding from the perspectiveof principles. It may be understood that the division of the submatricesA, B, C, D, and E is not limited to the foregoing division manner. In animplementation, C is an all zero matrix, E is an identity matrix, andstructures of C and E are known. Therefore, an LDPC matrix may berepresented in a simplified form without using all of the submatrices A,B, C, D, and E. For example, the LDPC matrix may be represented in asimplified form by the submatrices A, B, and D, by the submatrices A, B,C, and D, or by the submatrices A, B, D, and E. In anotherimplementation, because the submatrix B includes one or more weight-1columns, for the one or more weight-1 columns in the submatrix B, astructure is relatively definite. Therefore, the one or more weight-1columns may not be used to represent the LDPC matrix. For example, thesubmatrix A, some columns in the submatrix B, and corresponding columnsin the submatrix D may be used to represent the LDPC matrix.

When an LDPC matrix having the raptor-like structure is used forencoding, a possible implementation is that the part of the matrixincluding the submatrices A and B, namely a core matrix, may first beused in encoding to obtain one or more parity bits corresponding to thesubmatrix B. Then, the entire LDPC matrix is used in encoding to obtainone or more parity bits corresponding to the submatrix E. Because thesubmatrix B may include a submatrix B′ with bi-diagonal structure andone or more weight-1 columns, during encoding, parity bits correspondingto the submatrix B′ may be first obtained, and parity bits correspondingto the weight-1 columns may be then obtained.

An example of an encoding scheme is provided below. Assuming that thecore matrix including the submatrices A and B is H_(core). The matrix Bhas a structure of 20 c in FIG. 2. A last row and a last column of theH_(core) are removed. In other words, a weight-1 column and a row inwhich the non-zero-element in the weight-1 column is located are removedfrom the H_(core) to obtain a matrix H_(core)-dual. Parity bits part ofthe H_(core)-dual is represented as H_(e)=[H_(e1) H_(e2)], where H_(e1)is a weight-3 column, and H_(e2) has a bi-diagonal structure. Accordingto a definition of the LDPC matrix, H_(core-dual)·[S P_(e)]^(T)=0, whereS is an input sequence and is represented by a vector of informationbits, P_(e) is a vector of parity bits, and [S P_(e)]^(T) represents atransposed matrix formed by the input sequence S and P_(e). Therefore,parity bits corresponding to H_(core-dual) may be first calculated basedon the input sequence S and H_(core-dual), where the input sequence Sincludes all information bits. Then, parity bits corresponding to theone or more weight-1 columns in the submatrix B are calculated based onthe parity bits corresponding to H_(core-dual) and the input sequence S.In this case, all parity bits corresponding to the submatrix B may beobtained. Parity bits corresponding to the submatrix E are obtained byencoding the submatrix D based on the input sequence S and the paritybits corresponding to the submatrix B, to obtain all information bitsand all parity bits. These bits constitute an encoded sequence, namely,an LDPC codeword.

The LDPC code may further include a shortening operation or a puncturingoperation on the encoded sequence. The shortened bits or punctured bitsare not sent.

Shortening is usually performed starting from the last bit of theinformation bits, and may be performed in different manners. Forexample, if a quantity of shortened bits is s₀, the last so bits in theinput sequence S may be set as known bits, for example, set to 0, null,or other value, to obtain an input sequence S′. Then, the input sequenceS′ is encoded by using an LDPC matrix. For another example, the last (s₀mod Z) bits in the input sequence S may alternatively be set as knownbits, for example, set as zero, null, or some other value, to obtain aninput sequence S′. The last [s₀/Z] columns in the submatrix A aredeleted to obtain an LDPC matrix H′, and the input sequence S′ isencoded by using the LDPC matrix H′; or the last [sea] columns in thesubmatrix A do not participate in encoding of the input sequence S′.After the encoding, the shortened bits are not sent.

Puncturing may be performed on built-in puncture bit(s) or parity bit(s)in the input sequence. Puncturing parity bit(s) is/are usually performedstarting from the last bit in the parity bits. Alternatively, puncturingparity bit(s) may be performed according to a preset puncturing order ofthe system. A possible implementation is as follows: The input sequenceis first encoded, and then, last p bits in the parity bits is/areselected based on a quantity p of bits that need to be punctured, or pbits is/are selected based on the preset puncturing order of the system.The p bits is/are not sent. In another possible implementation,alternatively, p columns in a matrix that correspond to the puncturedbits and p rows in which nonzero elements in the columns are located maybe determined. These rows and columns do not participate in encoding,and no corresponding parity bits are generated.

It should be noted that the encoding implementation described herein ismerely an example, and other conventionally known encodingimplementations may alternatively be used based on the base graph and/orthe base matrix provided in embodiments of this application. This is notlimited in this application. Decoding in this application may beperformed in a plurality of decoding methods, for example, a min-sum(MS) decoding method or a belief propagation decoding method may beused. The MS decoding method is sometimes referred to as a Flood MSdecoding method. For example, the input sequence is initialized and theniteration processing is performed. Hard decision detection is performedafter the iteration, and a check is performed on a hard decision result.If a decoding result satisfies a check equation, the decoding succeeds,the iteration ends, and the decision result is output. If the decodingresult does not satisfy the check equation, iteration processing isperformed again within a maximum quantity of iterations. If a checkstill does not pass when the maximum quantity of iterations is reached,the decoding fails. A principle of the MS decoding is conventionallyknown, and details are not described herein.

It should be noted that the decoding method described herein is merelyan example, and other known decoding methods may alternatively be usedbased on the base graph and/or the base matrix provided in thisapplication. The decoding method is not limited in this application.

An LDPC codeword is obtained depending on the design of a base graph ora base matrix. For example, a performance upper limit of an LDPC codemay be determined by performing density evolution on the base graph orthe base matrix. An error floor of the LDPC code is determined based ona shift value in the base matrix. The encoding or decoding performancecan be improved and the error floor can be lowered by properly designingthe base graph or the base matrix. In the wireless communicationsystems, code length is flexible, for example, 2560 bits or 38400 bits.FIG. 3a shows an example of a base graph for an LDPC code. FIGS. 3b -1to 3 b-8 show examples of base matrices corresponding to the base graphin FIG. 3a . The base matrices may satisfy performance requirements of aplurality of block lengths. For ease of description and understanding,column indexes and row indexes are respectively shown on the uppermostside and the leftmost side in FIG. 3a and FIGS. 3b -1 to 3 b-8.

Similar to FIG. 1, elements in base matrices in FIGS. 3b -1 to 3 b-8 arein a one-to-one correspondence with the base graph in FIG. 3a ,respectively. A zero-element in the base graph of FIG. 3a has a sameposition in any one of the base matrices in FIGS. 3b -1 to 3 b-8. In thebase matrices, a zero-element is represented by the value of −1 or“null”. A non-zero-element in row i and column j, whose value is 1 inthe base graph of FIG. 3a , corresponds to a non-zero element at a sameposition in any one of the base matrices. The non-zero-element isrepresented by a value V_(i,j). V_(i,j) may be defined by a system, maybe predefined, or may be obtained based on a shift value P_(i,j) and alifting factor Z. P_(i,j) is a shift value corresponding to apredetermined or a particular lifting factor Z. P_(i,j) may be obtainedbased on Z and V_(i,j). In an implementation, P_(i,j) and V_(i,j)satisfy the following relationship:

P _(i,j)=mod(V _(i,j) ,Z)

where i and j represent a row index and a column index of the non-zeroelement, and indicate a location of the element in the any one of thebase matrices. V_(i,j) may be, for example, a shift value correspondingto a maximum lifting factor Z_(max). Z_(max) is a maximum value in avalue set of Z. A zero-element the element in the base matrix may bereplaced with a Z×Z all zero matrix. A non-zero-element may be replacedwith a Z×Z circular permutation matrix having the shift value ofP_(i,j). In this way, a parity check matrix H for the LDPC code isobtained.

FIG. 4 is a schematic performance diagram of an LDPC code shown in FIG.3a . In the performance diagram shown in FIG. 4, encoding performancecurves using any one of matrices shown in FIGS. 3b -1 to 3 b-8 areshown. The horizontal coordinate represents a length of an informationbit sequence in units of bits, and the vertical coordinate is asignal-to-noise ratio (Es/N0) for a symbol required to reach acorresponding block error rate (BLER). Two lines of each code ratecorrespond to two BLERs 0.01 and 0.0001. For a same code rate, 0.01 iscorresponding to an upper curve, and 0.0001 is corresponding to a lowercurve. If the curves are smooth, it indicates that the matrix hasrelatively high performance in cases of different block lengths.

In the base graph of FIG. 3a , numbers 0 to 51 in the uppermost row arecolumn indexes, and correspond to column 0 to column 51 of the basegraph, respectively. Numbers 0 to 41 in the leftmost column are rowindexes, and correspond to row 0 to row 41 of the base graph,respectively. That is, the base graph has a size of 42 rows and 52columns.

As mentioned above, a combination of the submatrix A and the submatrix Bmay be considered as a core matrix of the base graph for the LDPC code,and the core matrix may be used for high code-rate encoding. As shown inFIG. 3a , a matrix of 7 rows and 17 columns in the upper corner of thebase graph may be considered as the core matrix of the base graph. Thecore matrix includes the submatrix A and the submatrix B. The submatrixA is a matrix of 7 rows and 10 columns, and is constituted by row 0 torow 6 and column 0 to column 9 of the base matrix in FIG. 3a . Thesubmatrix B is a matrix of 7 rows and 7 columns, and is constituted byrow 0 to row 6 and column 10 to column 16 of the base matrix in FIG. 3a.

In another implementation, a matrix constituted by 7 rows and 14columns, or a matrix constituted by 7 rows and 15 columns, or a matrixconstituted by 7 rows and 16 columns, at an upper left corner in thebase graph shown in FIG. 3a , may be considered as the core part. Inother words, in the base graph shown in FIG. 3a , a matrix constitutedby row 0 to row 6 and column 0 to column 13, or a matrix constituted byrow 0 to row 6 and column 0 to column 14, or a matrix constituted by row0 to row 6 and column 0 to column 15, may be considered as the corepart. Correspondingly, a part in any one of the matrices shown in FIGS.3b -1 to 3 b-8 that corresponds to a core part in the base graph of FIG.3a may alternatively be considered as a core part.

In an implementation, the submatrix A may include one or more built-inpuncture columns. For example, the submatrix A may include two built-inpuncture columns. In this case, after the puncturing, a code rate thatcan be supported by the core matrix is ⅔. The submatrix B may includeone weight-1 column. To be specific, a column weight of the first columnin the submatrix B is 3 (column 10 in the core matrix). A column weightof the second column in the submatrix B is 5 (column 11 in the corematrix). The second column to the fourth column (column 11 to column 13in the core matrix) and row 0 to row 3 in the submatrix B are of abi-diagonal structure, where column weights of the third column and thefourth column (column 12 and column 13 in the core matrix) are 2. Thesubmatrix B further includes three weight-1 columns (column 14 to column16 in the core matrix).

In an implementation, the submatrix A may correspond to system bits,sometimes is also referred to as information bits, and has a size ofm_(A) rows and 10 columns, where m_(A)=5. The submatrix A is constitutedby elements in row 0 to row 4 and column 0 to column 9 in the base graphin FIG. 3 a.

In an implementation, the submatrix B may correspond to parity bits, andhave a size of m_(A) rows and m_(A) columns. The submatrix B isconstituted by elements in row 0 to row 6 and column 10 to column 16 inthe base graph in FIG. 3 a.

To obtain a flexible code rate, the submatrix C, the submatrix D, andthe submatrix E of corresponding sizes may be added based on the corematrix, to obtain different code rates. Because the submatrix C is azero matrix, the submatrix E is an identity matrix, and sizes of thesubmatrices are mainly determined based on the code rates, structuresare relatively fixed. The encoding/decoding performance is mainlyaffected by the core matrix and the submatrix D. Rows and columns areadded based on the core matrix, to form corresponding parts C, D, and E,thereby obtaining different code rates.

A quantity m_(D) of columns in the submatrix D is a sum of quantities ofcolumns in the submatrix A and the submatrix B. A quantity of rows inthe submatrix D is mainly related to a code rate. Using the base graphin FIG. 3a as an example, the submatrix D has 17 columns. If a code ratesupported by the LDPC code is R_(m), the base graph or the base matrixfor the LDPC code has m rows and n columns, where n=n_(A)/R_(m)+p,m=n−n_(A)=n_(A)/R_(m)+p−n_(A), and p is the quantity of built-inpuncture columns. The code rate supported by the LDPC code may beobtained based on the formula. If a lowest code rate is R_(m)=⅓ and thequantity p of built-in puncture columns is 2, in the example of the basegraph in FIG. 3a as an example, n=52, m=42, and a quantity m_(D) of rowsin the submatrix D may be up to m−m_(A)=42−7=35, so that 0≤m_(D)≤35.

Using the base graph in FIG. 3a as an example, the submatrix D mayinclude m_(D) rows in row 7 to row 41 in the base graph.

In this application, if there is at most one non-zero-element in eachcolumn for two adjacent rows in the base graph, the two rows areorthogonal. In other columns different from some columns for twoadjacent rows in the base graph, if there is at most onenon-zero-element in each column of the other columns for two adjacentrows, the two adjacent rows are quasi-orthogonal. For example, for twoadjacent rows, in each column other than the built-in puncture columns,if there is only one non-zero-element, it may be considered that the twoadjacent rows are quasi-orthogonal.

Row 7 to row 41 in the base graph in FIG. 3a may include a plurality ofrows in a quasi-orthogonal structure and at least two rows in anorthogonal structure. For example, row 32 and row 33 in the base graphin FIG. 3a are orthogonal, row 34 and row 35 are orthogonal, and rows36, 37, and 38 are orthogonal. For any two adjacent rows, in othercolumns different from the built-in puncture column, if there is at mostone non-zero-element in each column, the two adjacent rows satisfy aquasi-orthogonal structure. If the built-in puncture columns areincluded, there is at most one non-zero-element in any one of columns,the two adjacent rows satisfy an orthogonal structure.

If m_(D)=15, the submatrix D in the base graph of the LDPC code has 15rows and 17 columns, and may be a matrix constituted by row 7 to row 21and column 0 to column 16 in the base graph of FIG. 3a . A correspondingcode rate supported by the LDPC code may be obtained based on theforegoing calculation formula.

The submatrix E is an identity matrix of 15 rows and 15 columns, and thesubmatrix C is an all zero matrix of 7 rows and 15 columns.

If m_(D)=19, the submatrix D in the base graph of the LDPC code has 19rows and 17 columns, and may be a matrix constituted by row 7 to row 25and column 0 to column 16 in the base graph of FIG. 3a . A correspondingcode rate supported by the LDPC code may be obtained based on theforegoing calculation formula. At this code rate, the base graph of theLDPC code is corresponding to a matrix constituted by row 0 to row 25and column 0 to column 16 in the base graph of FIG. 3a . The submatrix Eis an identity matrix of 16 rows and 16 columns, and the submatrix C isan all zero matrix of 7 rows and 16 columns. The same is true if m_(D)is other value, details are not described.

In a design, row/column permutation may be performed on the base graphand/or the base matrix. Row/column permutation maybe row permutation,column permutation, or row permutation and column permutation. Therow/column permutation does not change a row weight or a column weight,and does not change a quantity of non-zero-elements either. Therefore, abase graph and/or a base matrix obtained by performing row/columnpermutation have/has limited impact on system performance. As a whole,the impact on the system performance due to the row/column permutationis acceptable and is within a tolerance range. For example, theperformance decreases within a tolerance range in some scenarios or insome ranges, while in some scenarios or in some ranges, the performanceimproves to some extent, and overall performance is not greatlyaffected.

For example, row 34 and row 36 of the base graph in FIG. 3a may beinterchanged, and column 44 and column 45 may be interchanged. Foranother example, the submatrix D includes m_(D) rows in a matrix F. Rowinterchange may not be performed on the m_(D) rows, or row interchangemay be performed on one or more of the m_(D) rows. The submatrix E isstill of a diagonal structure, and no row interchange or columninterchange is performed on the submatrix E. For example, rowinterchange is performed on row 27 and row 29 in the matrix F. Thesubmatrix D includes the m_(D) rows in the matrix F, and the submatrix Eis still of a diagonal structure. It may be understood that if the basegraph or the base matrix includes the submatrix D, when columninterchange is performed on the core matrix, column interchange needs tobe performed correspondingly on the submatrix D.

Matrices shown in FIGS. 3b -1 to 3 b-8 are examples of the base matricescorresponding to the base graph in FIG. 3a . A location of anon-zero-element in row i and column j in the base graph in FIG. 3a isthe same as that in the matrices shown in FIGS. 3b -1 to 3 b-8. A shiftvalue of the non-zero-element is V_(i,j). A zero-element is representedas a value −1 or null in the base matrix. A corresponding part of thesubmatrix D in the base matrix may include m_(D) rows in row 7 to row 41in any one of the base matrices and values of m_(D) may be selectedbased on different code rates. It may be understood that if the basegraph is a matrix obtained by performing row/column transformation onthe base graph in FIG. 3a , accordingly, the base matrix is acorresponding matrix obtained by performing row/column transformation.

In a possible design, because structures of the submatrices C and E arerelatively fixed, the base graph/the base matrix of the LDPC code may berepresented by using the submatrices A, B, and D, that is, row 0 to row41 and column 0 to column 16 in any of the matrix shown in FIG. 3a orFIGS. 3b -1 to 3 b-8.

In a possible design, because column 14 to column 51 have relativelydefinite structure, the base graph/the base matrix of the LDPC code maybe represented in a simplified form by using row 0 to row 41 and column0 to column 13 in any of the matrix shown in FIG. 3a or FIGS. 3b -1 to 3b-8.

In a possible design, the base graph/the base matrix of the LDPC codemay be represented by using row 0 to row 41 and column 0 to column 13plus some of column 14 to column 51 in any of the matrix shown in FIG.3a or FIGS. 3b -1 to 3 b-8. For example, the base graph/the base matrixof the LDPC code may be represented by using row 0 to row 41 and column0 to column 15 or row 0 to row 41 and column 0 to column 14 in any ofthe matrices shown in FIG. 3a or FIGS. 3b -1 to 3 b-8.

In a possible design, the base matrix of the LDPC code may include row 0to row 6 and column 0 to column 16 in any one of the matrices shown inFIGS. 3b -1 to 3 b-8. In this case, a matrix constituted by row 0 to row6 and column 0 to column 16 in any one of the matrices shown in FIGS. 3b-1 to 3 b-8 may be used as a core part of the base matrix. In thisdesign, a structure of another part, for example, submatrices C, D, andE, of the base matrix of the LDPC code is not limited. For example, anystructure shown in FIGS. 3b -1 to 3 b-8 or another matrix design may beused.

In another possible design, the base matrix of the LDPC code may includea matrix constituted by row 0 to row m−1 and column 0 to column n−1 inany one of the matrices shown in FIGS. 3b -1 to 3 b-8, where 7≤m≤42, mis an integer, 18≤n≤52, and n is an integer.

In this design, a structure of another part of the base matrix of theLDPC code is not limited. For example, any structure shown in FIGS. 3b-1 to 3 b-8 or another matrix design may be used.

In still another possible design, the base matrix of the LDPC code mayinclude row 0 to row 6 and some columns of column 0 to column 16 in anyone of the matrices shown in FIGS. 3b -1 to 3 b-8. For example, the corepart (row 0 to row 6 and column 0 to column 16) of the matrices shown inFIGS. 3b -1 to 3 b-8 may be shortened and/or punctured. In animplementation, the base matrix of the LDPC code may not includecolumn(s) corresponding to shortened and/or punctured bit(s).

In this design, other part of the base matrix of the LDPC code is notlimited. For example, a structure shown in FIGS. 3b -1 to 3 b-8 may beused, and other structures may be used as well.

In still another possible design, the base matrix of the LDPC code mayinclude a matrix constituted by row 0 to row m−1 and some columns ofcolumn 0 to column n−1 in any one of the matrices shown in FIGS. 3b -1to 3 b-8, where 7≤m≤42, m is an integer, 18≤n≤52, and n is an integer.For example, shortening operation and/or puncturing operation may beperformed on row 0 to row m−1 and column 0 to column n−1 of any one ofmatrices shown in FIGS. 3b -1 to 3 b-8. In an implementation, the basematrix of the LDPC code may not include the column(s) corresponding tothe shortened and/or punctured bit(s). In this design, other part of thebase matrix of the LDPC code is not limited. For example, a structureshown in any of FIGS. 3b -1 to 3 b-8 may be used, and other structuresmay be used as well.

In an implementation, the shortening operation may be shorteninginformation bits. Using any one of the matrices shown in FIGS. 3b -1 to3 b-8 as an example, one or more columns of column 0 to column 9 areshortened. In this case, the base matrix of the LDPC code may notinclude the one or more shortened columns in any one of the matricesshown in FIGS. 3b -1 to 3 b-8. For example, if column 9 is shortened,the base matrix of the LDPC code may include column 0 to column 8 andcolumn 10 to column 16 in any one of the matrices in FIGS. 3b -1 to 3b-8.

In another implementation, the puncturing operation may be puncturingparity bits. Using any one of the matrices shown in FIGS. 3b -1 to 3 b-8as an example, one or more columns of column 10 to column 16 arepunctured. In this case, the base matrix of the LDPC code may notinclude the one or more punctured columns in any one of the matricesshown in FIGS. 3b -1 to 3 b-8. For example, if column 16 is punctured,the base matrix of the LDPC code may include column 0 to column 15 inany one of the matrices shown in FIGS. 3b -1 to 3 b-8.

To support different block lengths, the LDPC code needs differentlifting factors Z. In a possible design, different base matrices may beused for different lifting factors, to achieve relatively highperformance. For example, the lifting factor is Z=a×2^(j), where 0≤j<7and a ∈{2, 3, 5, 7, 9, 11, 13, 15}. Table 1A shows a possibly supportedlifting factor set {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,18, 20, 22, 24, 26, 28, 30, 32, 36, 40, 44, 48, 52, 56, 60, 64, 72, 80,88, 96, 104, 112, 120, 128, 144, 160, 176, 192, 208, 224, 240, 256, 288,320, 352, 384}. Each of cells except for the uppermost row and theleftmost column represents a value of Z corresponding to values ofcorresponding a and j. For example, for a column a=2 and a row j=1, Z is4. For another example, for a=11 and j=3, Z is 88. By analogy, detailsare not described.

TABLE 1A Z a = 2 a = 3 a = 5 a = 7 a = 9 a = 11 a = 13 a = 15 j = 0 2 35 7 9 11 13 15 j = 1 4 6 10 14 18 22 26 30 j = 2 8 12 20 28 36 44 52 60j = 3 16 24 40 56 72 88 104 120 j = 4 32 48 80 112 144 176 208 240 j = 564 96 160 224 288 352 j = 6 128 192 320 j = 7 256 384

It may be understood that Table 1A merely shows a form of describing alifting factor set. Actual product implementation is not limited to theform in Table 1A, and the lifting factors may have anotherrepresentation form.

For example, each a value is corresponding to a set of lifting factor.The lifting factor set may be identified by a set index. For example,Table 1B shows another representation form of lifting factor set.

TABLE 1B Set index Set of lifting factors 1 {2, 4, 8, 16, 32, 64, 128,256} 2 {3, 6, 12, 24, 48, 96, 192, 384} 3 {5, 10, 20, 40, 80, 160, 320}4 {7, 14, 28, 56, 112, 224} 5 {9, 18, 36, 72, 144, 288} 6 {11, 22, 44,88, 176, 352} 7 {13, 26, 52, 104, 208} 8 {15, 30, 60, 120, 240}

The lifting factor set supported by the base graph may include alllifting factors or some lifting factors in Table 1A or Table 1B. Forexample, the lifting factor set may be {24, 26, 28, 30, 32, 36, 40, 44,48, 52, 56, 60, 64, 72, 80, 88, 96, 104, 112, 120, 128, 144, 160, 176,192, 208, 224, 240, 256, 288, 320, 352, 384}. In other words, Z isgreater than or equal to 24. For another example, the lifting factor setmay be a union set of {24, 26, 28, 30, 32, 36, 40, 44, 48, 52, 56, 60,64, 72, 80, 88, 96, 104, 112, 120, 128, 144, 160, 176, 192, 208, 224,240, 256, 288, 320, 352, 384} and one or more of {2, 3, 4, 5, 6, 7, 8,9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 22}. It should be noted that thisis merely an example herein. The lifting factor set supported by thebase graph may be divided into different subsets based on a value of a.For example, if a=2, a subset of lifting factors Z may include one ormore of {2, 4, 8, 16, 32, 64, 128, 256}; for another example, if a=3, asubset of lifting factors Z may include one or more of {3, 6, 12, 24,48, 96, 192, 384}; and so on.

The lifting factor set supported by the base graph may be divided basedon different values of a, and a corresponding base matrix is determined.

If a=2 or a value of the lifting factor Z is one of {2, 4, 8, 16, 32,64, 128, 256}, the base matrix may include the row 0 to row 6 and column0 to column 16 in any one of the matrices shown in FIGS. 3b -1 to 3 b-8;or the base matrix includes row 0 to row m−1 and column 0 to column n−1in a matrix shown in FIG. 3b -1, where 7≤m≤42, m is an integer, 17≤n≤52,and n is an integer; or the base matrix includes row 0 to row m−1 andsome columns of column 0 to column n−1 in a matrix shown in FIG. 3b -1,where 7≤m≤42, m is an integer, 17≤n≤52, and n is an integer.

If a=3 or a value of the lifting factor Z is one of {3, 6, 12, 24, 48,96, 192, 384}, the base matrix may include row 0 to row 6 and column 0to column 16 in a matrix shown in FIG. 3b -2; or the base matrixincludes row 0 to row m−1 and column 0 to column n−1 in a matrix shownin FIG. 3b -2, where 7≤m≤42, m is an integer, 17≤n≤52, and n is aninteger; or the base matrix includes row 0 to row m−1 and some columnsof column 0 to column n−1 in a matrix shown in FIG. 3b -2, where 7≤m≤42,m is an integer, 17≤n≤52, and n is an integer.

For example, a base matrix PCM includes row 0 to row 41 and column 0 tocolumn 13, or column 0 to column 14, or column 0 to column 15 in FIG. 3b-2.

If a=5 or a value of the lifting factor Z is one of {5, 10, 20, 40, 80,160, 320}, the base matrix may include row 0 to row 6 and column 0 tocolumn 16 in a matrix shown in FIG. 3 b-3; or the base matrix includesrow 0 to row m−1 and column 0 to column n−1 in a matrix shown in FIG. 3b-3, where 7≤m≤42, m is an integer, 17≤n≤52, and n is an integer; or thebase matrix includes row 0 to row m−1 and some columns of column 0 tocolumn n−1 in a matrix shown in FIG. 3b -3, where 7≤m≤42, m is aninteger, 17≤n≤52, and n is an integer.

If a=7 or a value of the lifting factor Z is one of {7, 14, 28, 56, 112,224}, the base matrix may include row 0 to row 6 and column 0 to column16 in a matrix shown in FIG. 3b -4; or the base matrix includes row 0 torow m−1 and column 0 to column n−1 in a matrix shown in FIG. 3b -4,where 7≤m≤42, m is an integer, 17≤n≤52, and n is an integer; or the basematrix includes row 0 to row m−1 and some columns of column 0 to columnn−1 in a matrix shown in FIG. 3b -4, where 7≤m≤42, m is an integer,17≤n≤52, and n is an integer.

If a=9 or a value of the lifting factor Z is one of {9, 18, 36, 72, 144,288}, the base matrix may include row 0 to row 6 and column 0 to column16 in a matrix shown in FIG. 3b -5; or the base matrix includes row 0 torow m−1 and column 0 to column n−1 in a matrix shown in FIG. 3b -5,where 7≤m≤42, m is an integer, 17≤n≤52, and n is an integer; or the basematrix includes row 0 to row m−1 and some columns of column 0 to columnn−1 in a matrix shown in FIG. 3b -5, where 7≤m≤42, m is an integer,17≤n≤52, and n is an integer.

If a=11 or a value of the lifting factor Z is one of {11, 22, 44, 88,176, 352}, the base matrix may include row 0 to row 6 and column 0 tocolumn 16 in a matrix shown in FIG. 3b -6; or the base matrix includesrow 0 to row m−1 and column 0 to column n−1 in a matrix shown in FIG. 3b-6, where 7≤m≤42, m is an integer, 17≤n≤52, and n is an integer; or thebase matrix includes row 0 to row m−1 and some columns of column 0 tocolumn n−1 in a matrix shown in FIG. 3b -6, where 7≤m≤42, m is aninteger, 17≤n≤52, and n is an integer.

If a=13 or a value of the lifting factor Z is one of {13, 26, 52, 104,208}, the base matrix may include row 0 to row 6 and column 0 to column16 in a matrix shown in FIG. 3b -7; or the base matrix includes row 0 torow m−1 and column 0 to column n−1 in a matrix shown in FIG. 3b -7,where 7≤m≤42, m is an integer, 17≤n≤52, and n is an integer; or the basematrix includes row 0 to row m−1 and some columns of column 0 to columnn−1 in a matrix shown in FIG. 3b -7, where 7≤m≤42, m is an integer,17≤n≤52, and n is an integer.

If a=15 or a value of the lifting factor Z is one of {15, 30, 60, 120,240}, the base matrix may include row 0 to row 6 and column 0 to column16 in a matrix 3 b-8; or the base matrix includes row 0 to row m−1 andcolumn 0 to column n−1 in a matrix shown in FIG. 3b -8, where 7≤m≤42, mis an integer, 17≤n≤52, and n is an integer; or the base matrix includesand some columns of column 0 to column n−1 in a matrix shown in FIG. 3b-8, where 7≤m≤42, m is an integer, 17≤n≤52, and n is an integer.

Optionally, for a base matrix for an LDPC code, shift values ofnon-zero-elements in one or more columns may be increased or decreasedby a compensation value Offset_(s), without greatly affecting the systemperformance. Compensation values of non-zero-elements in differentcolumns may be the same or different. For example, to compensate one ormore columns in a matrix, compensation values for different columns maybe the same or different. This is not limited in this application.

Not greatly affecting the system performance means that the impact onthe system performance is acceptable and is within a tolerance range.For example, the performance decreases within a tolerance range in somescenarios or in some ranges. However, in some scenarios or in someranges, the performance improves to some extent. Overall performance isnot greatly affected.

For example, the compensation value Offset_(s) is added to or subtractedfrom each shift value greater than or equal to 0 in column s in any oneof the matrices shown in FIGS. 3b -1 to 3 b-8, to obtain a compensatedmatrix Hs, where Offset_(s) is an integer greater than or equal to 0,and s is an integer greater than or equal to 0 and less than 11.Compensation values Offset_(s) for one or more columns may be the sameor different.

In the performance diagram shown in FIG. 4, based on performance curvesof encoding matrices shown in FIG. 3b -1 and FIG. 3b -2, a horizontalcoordinate represents a length of an information bit sequence, and aunit of the length is bit, and a vertical coordinate is a symbolsignal-to-noise ratio (Es/N0) required to reach a corresponding BLER.Two lines of each code rate are corresponding to two cases of BLERs 0.01and 0.0001. At a same code rate, 0.01 is corresponding to an uppercurve, and 0.0001 is corresponding to a lower curve. If the curves aresmooth, it indicates that the matrix has relatively high performance incases of different block lengths.

FIG. 1 to FIG. 3a and FIGS. 3b -1 to 3 b-8 show structures of the basegraph and the base matrix that are related to the LDPC code. Tosufficiently describe designs of the base graph and/or the base matrixin the implementations of the present application, the structure of thebase matrix may be represented in another form that can be identified bythe system, for example, in a tabular form.

In a design, the base graph shown by 10 a in FIG. 1 is a matrix of 7rows and 10 columns, and related parameters may be represented in Table2.

TABLE 2 (Corresponding to 10a in FIG. 1) Row number Row weight Columnindex of non-zero-element 0 8 0, 1, 2, 3, 6, 9, 10, 11 1 10 0, 3, 4, 5,6, 7, 8, 9, 11, 12 2 8 0, 1, 3, 4, 8, 10, 12, 13 3 10 1, 2, 4, 5, 6, 7,8, 9, 10, 13 4 4 0, 1, 11, 14 5 6 0, 1, 5, 7, 11, 15 6 6 0, 5, 7, 9, 11,16

It may be understood that because column 14 to column 16 in the basegraph 10 a are columns whose column weight is 1, and locations of thecolumns are relatively fixed or easily determined, locations ofnon-zero-elements in column 14 to column 16 may not be recorded in Table2, but are recorded in another form.

In a design, using the base matrices shown in FIGS. 3b -1 to 3 b-8 asexamples, parameters related to the base matrices may be respectivelyrepresented in Table 3b-1 to Table 3b-8.

TABLE 3b-1 (Corresponding to FIG. 3b-1) Row number Row Column index ofShift value of (row index) weight non-zero-element non-zero-element 0 80, 1, 2, 3, 6, 9, 0, 0, 0, 0, 0, 0, 10, 11 0, 0 1 10 0, 3, 4, 5, 6, 7,183, 27, 0, 0, 222, 8, 9, 11, 12 0, 0, 204, 0, 0 2 8 0, 1, 3, 4, 8, 162,164, 117, 44, 10, 12, 13 159, 1, 0, 0 3 10 1, 2, 4, 5, 6, 7, 168, 22,57, 188, 173, 8, 9, 10, 13 110, 85, 223, 0, 0 4 4 0, 1, 11, 14 0, 44,70, 0 5 6 0, 1, 5, 7, 11, 15 0, 221, 215, 45, 171, 0 6 6 0, 5, 7, 9, 11,16 0, 170, 23, 60, 241, 0 7 6 1, 5, 7, 11, 13, 17 0, 27, 36, 157, 153, 08 4 0, 1, 12, 18 0, 126, 16, 0 9 5 1, 8, 10, 11, 19 0, 126, 251, 76, 010 5 0, 1, 6, 7, 20 0, 49, 162, 248, 0 11 5 0, 7, 9, 13, 21 0, 4, 143,236, 0 12 4 1, 3, 11, 22 0, 4, 151, 0 13 5 0, 1, 8, 13, 23 0, 235, 95,173, 0 14 5 1, 6, 11, 13, 24 0, 51, 177, 63, 0 15 4 0, 10, 11, 25 0, 69,63, 0 16 5 1, 9, 11, 12, 26 0, 106, 117, 67, 0 17 5 1, 5, 11, 12, 27 0,239, 82, 222, 0 18 4 0, 6, 7, 28 0, 41, 214, 0 19 4 0, 1, 10, 29 0, 71,123, 0 20 4 1, 4, 11, 30 0, 228, 3, 0 21 4 0, 8, 13, 31 0, 155, 240, 022 3 1, 2, 32 0, 75, 0 23 4 0, 3, 5, 33 0, 247, 96, 0 24 4 1, 2, 9, 340, 71, 227, 0 25 3 0, 5, 35 0, 83, 0 26 5 2, 7, 12, 13, 36 0, 12, 126,152, 0 27 3 0, 6, 37 0, 220, 0 28 4 1, 2, 5, 38 0, 98, 70, 0 29 3 0, 4,39 0, 13, 0 30 5 2, 5, 7, 9, 40 0, 120, 87, 230, 0 31 3 1, 13, 41 0,110, 0 32 4 0, 5, 12, 42 0, 5, 115, 0 33 4 2, 7, 10, 43 0, 210, 110, 034 4 0, 12, 13, 44 0, 84, 57, 0 35 4 1, 5, 11, 45 0, 224, 137, 0 36 4 0,2, 7, 46 0, 29, 3, 0 37 3 10, 13, 47 0, 129, 0 38 4 1, 5, 11, 48 0, 125,123, 0 39 4 0, 7, 12, 49 0, 154, 247, 0 40 4 2, 10, 13, 50 0, 85, 113, 041 4 1, 5, 11, 51 0, 97, 230, 0

TABLE 3b-2 (Corresponding to FIG. 3b-2) Row number Row Column index ofShift value of (row index) weight non-zero-element non-zero-element 0 80, 1, 2, 3, 6, 9, 0, 0, 0, 0, 0, 0, 0, 0 10, 11 1 10 0, 3, 4, 5, 6, 7,187, 56, 0, 0, 45, 0, 8, 9, 11, 12 0, 18, 0, 0 2 8 0, 1, 3, 4, 8, 10,179, 171, 54, 158, 116, 12, 13 1, 0, 0 3 10 1, 2, 4, 5, 6, 7, 106, 62,52, 185, 80, 8, 9, 10, 13 81, 66, 163, 0, 0 4 4 0, 1, 11, 14 0, 89, 43,0 5 6 0, 1, 5, 7, 11, 15 0, 109, 191, 42, 142, 0 6 6 0, 5, 7, 9, 11, 160, 163, 112, 100, 131, 0 7 6 1, 5, 7, 11, 13, 17 0, 60, 78, 92, 183, 0 84 0, 1, 12, 18 0, 123, 58, 0 9 5 1, 8, 10, 11, 19 0, 180, 55, 49, 0 10 50, 1, 6, 7, 20 0, 134, 184, 158, 0 11 5 0, 7, 9, 13, 21 0, 153, 164,189, 0 12 4 1, 3, 11, 22 0, 167, 154, 0 13 5 0, 1, 8, 13, 23 0, 187,166, 67, 0 14 5 1, 6, 11, 13, 24 0, 29, 67, 145, 0 15 4 0, 10, 11, 25 0,21, 16, 0 16 5 1, 9, 11, 12, 26 0, 122, 113, 98, 0 17 5 1, 5, 11, 12, 270, 99, 112, 70, 0 18 4 0, 6, 7, 28 0, 135, 164, 0 19 4 0, 1, 10, 29 0,94, 90, 0 20 4 1, 4, 11, 30 0, 173, 59, 0 21 4 0, 8, 13, 31 0, 8, 143, 022 3 1, 2, 32 0, 42, 0 23 4 0, 3, 5, 33 0, 190, 72, 0 24 4 1, 2, 9, 340, 73, 111, 0 25 3 0, 5, 35 0, 188, 0 26 5 2, 7, 12, 13, 36 0, 0, 1,113, 0 27 3 0, 6, 37 0, 185, 0 28 4 1, 2, 5, 38 0, 41, 89, 0 29 3 0, 4,39 0, 36, 0 30 5 2, 5, 7, 9, 40 0, 141, 35, 124, 0 31 3 1, 13, 41 0,152, 0 32 4 0, 5, 12, 42 0, 145, 117, 0 33 4 2, 7, 10, 43 0, 68, 176, 034 4 0, 12, 13, 44 0, 92, 75, 0 35 4 1, 5, 11, 45 0, 189, 18, 0 36 4 0,2, 7, 46 0, 140, 179, 0 37 3 10, 13, 47 0, 19, 0 38 4 1, 5, 11, 48 0,44, 3, 0 39 4 0, 7, 12, 49 0, 111, 167, 0 40 4 2, 10, 13, 50 0, 27, 92,0 41 4 1, 5, 11, 51 0, 158, 156, 0

TABLE 3b-3 (Corresponding to FIG. 3b-3) Row number Row Column index ofShift value of (row index) weight non-zero-element non-zero-element 0 80, 1, 2, 3, 6, 9, 0, 0, 0, 0, 0, 0, 0, 0 10, 11 1 10 0, 3, 4, 5, 6, 7,8, 137, 124, 0, 0, 88, 0, 9, 11, 12 0, 55, 0, 0 2 8 0, 1, 3, 4, 8, 10,20, 94, 99, 9, 108, 12, 13 1, 0, 0 3 10 1, 2, 4, 5, 6, 7, 8, 38, 15,102, 146, 12, 9, 10, 13 57, 53, 46, 0, 0 4 4 0, 1, 11, 14 0, 136, 157, 05 6 0, 1, 5, 7, 11, 15 0, 131, 142, 141, 64, 0 6 6 0, 5, 7, 9, 11, 16 0,124, 99, 45, 148, 0 7 6 1, 5, 7, 11, 13, 17 0, 45, 148, 96, 78, 0 8 4 0,1, 12, 18 0, 65, 87, 0 9 5 1, 8, 10, 11, 19 0, 97, 51, 85, 0 10 5 0, 1,6, 7, 20 0, 17, 156, 20, 0 11 5 0, 7, 9, 13, 21 0, 7, 4, 2, 0 12 4 1, 3,11, 22 0, 113, 48, 0 13 5 0, 1, 8, 13, 23 0, 112, 102, 26, 0 14 5 1, 6,11, 13, 24 0, 138, 57, 27, 0 15 4 0, 10, 11, 25 0, 73, 99, 0 16 5 1, 9,11, 12, 26 0, 79, 111, 143, 0 17 5 1, 5, 11, 12, 27 0, 24, 109, 18, 0 184 0, 6, 7, 28 0, 18, 86, 0 19 4 0, 1, 10, 29 0, 158, 154, 0 20 4 1, 4,11, 30 0, 148, 104, 0 21 4 0, 8, 13, 31 0, 17, 33, 0 22 3 1, 2, 32 0, 4,0 23 4 0, 3, 5, 33 0, 75, 158, 0 24 4 1, 2, 9, 34 0, 69, 87, 0 25 3 0,5, 35 0, 65, 0 26 5 2, 7, 12, 13, 36 0, 100, 13, 7, 0 27 3 0, 6, 37 0,32, 0 28 4 1, 2, 5, 38 0, 126, 110, 0 29 3 0, 4, 39 0, 154, 0 30 5 2, 5,7, 9, 40 0, 35, 51, 134, 0 31 3 1, 13, 41 0, 20, 0 32 4 0, 5, 12, 42 0,20, 122, 0 33 4 2, 7, 10, 43 0, 88, 13, 0 34 4 0, 12, 13, 44 0, 19, 78,0 35 4 1, 5, 11, 45 0, 157, 6, 0 36 4 0, 2, 7, 46 0, 63, 82, 0 37 3 10,13, 47 0, 144, 0 38 4 1, 5, 11, 48 0, 93, 19, 0 39 4 0, 7, 12, 49 0, 24,138, 0 40 4 2, 10, 13, 50 0, 36, 143, 0 41 4 1, 5, 11, 51 0, 2, 55, 0

TABLE 3b-4 (Corresponding to FIG. 3b-4) Row number Row Column index ofShift value of (row index) weight non-zero-element non-zero-element 0 80, 1, 2, 3, 6, 9, 0, 0, 0, 0, 0, 0, 0, 0 10, 11 1 10 0, 3, 4, 5, 6, 7,8, 152, 115, 0, 0, 163, 0, 9, 11, 12 0, 186, 0, 0 2 8 0, 1, 3, 4, 8, 10,52, 149, 95, 136, 30, 1, 12, 13 0, 0 3 10 1, 2, 4, 5, 6, 7, 8, 3, 41,145, 171, 2, 188, 9, 10, 13 4, 180, 0, 0 4 4 0, 1, 11, 14 0, 178, 36, 05 6 0, 1, 5, 7, 11, 15 0, 116, 118, 213, 54, 0 6 6 0, 5, 7, 9, 11, 16 0,121, 215, 86, 220, 0 7 6 1, 5, 7, 11, 13, 17 0, 188, 88, 155, 135, 0 8 40, 1, 12, 18 0, 100, 136, 0 9 5 1, 8, 10, 11, 19 0, 157, 3, 195, 0 10 50, 1, 6, 7, 20 0, 20, 92, 134, 0 11 5 0, 7, 9, 13, 21 0, 66, 194, 133, 012 4 1, 3, 11, 22 0, 15, 59, 0 13 5 0, 1, 8, 13, 23 0, 49, 74, 187, 0 145 1, 6, 11, 13, 24 0, 60, 151, 154, 0 15 4 0, 10, 11, 25 0, 122, 55, 016 5 1, 9, 11, 12, 26 0, 128, 147, 14, 0 17 5 1, 5, 11, 12, 27 0, 141,131, 122, 0 18 4 0, 6, 7, 28 0, 52, 160, 0 19 4 0, 1, 10, 29 0, 8, 223,0 20 4 1, 4, 11, 30 0, 65, 104, 0 21 4 0, 8, 13, 31 0, 77, 93, 0 22 3 1,2, 32 0, 133, 0 23 4 0, 3, 5, 33 0, 18, 214, 0 24 4 1, 2, 9, 34 0, 78,43, 0 25 3 0, 5, 35 0, 106, 0 26 5 2, 7, 12, 13, 36 0, 191, 142, 47, 027 3 0, 6, 37 0, 166, 0 28 4 1, 2, 5, 38 0, 123, 150, 0 29 3 0, 4, 39 0,177, 0 30 5 2, 5, 7, 9, 40 0, 51, 140, 159, 0 31 3 1, 13, 41 0, 119, 032 4 0, 5, 12, 42 0, 81, 89, 0 33 4 2, 7, 10, 43 0, 100, 134, 0 34 4 0,12, 13, 44 0, 138, 34, 0 35 4 1, 5, 11, 45 0, 46, 212, 0 36 4 0, 2, 7,46 0, 189, 165, 0 37 3 10, 13, 47 0, 106, 0 38 4 1, 5, 11, 48 0, 176,144, 0 39 4 0, 7, 12, 49 0, 88, 141, 0 40 4 2, 10, 13, 50 0, 150, 6, 041 4 1, 5, 11, 51 0, 131, 52, 0

TABLE 3b-5 (Corresponding to FIG. 3b-5) Row number Row Column index ofShift value of (row index) weight non-zero-element non-zero-element 0 80, 1, 2, 3, 6, 9, 0, 0, 0, 0, 0, 0, 0, 0 10, 11 1 10 0, 3, 4, 5, 6, 7,8, 57, 6, 0, 0, 16, 0, 0, 9, 11, 12 95, 0, 0 2 8 0, 1, 3, 4, 8, 10, 141,25, 53, 132, 8, 1, 12, 13 0, 0 3 10 1, 2, 4, 5, 6, 7, 8, 77, 8, 117, 3,119, 55, 9, 10, 13 86, 21, 0, 0 4 4 0, 1, 11, 14 0, 70, 71, 0 5 6 0, 1,5, 7, 11, 15 0, 113, 8, 79, 37, 0 6 6 0, 5, 7, 9, 11, 16 0, 34, 136,127, 83, 0 7 6 1, 5, 7, 11, 13, 17 0, 13, 63, 142, 114, 0 8 4 0, 1, 12,18 0, 35, 67, 0 9 5 1, 8, 10, 11, 19 0, 16, 15, 21, 0 10 5 0, 1, 6, 7,20 0, 13, 114, 21, 0 11 5 0, 7, 9, 13, 21 0, 0, 96, 86, 0 12 4 1, 3, 11,22 0, 106, 20, 0 13 5 0, 1, 8, 13, 23 0, 84, 113, 47, 0 14 5 1, 6, 11,13, 24 0, 122, 51, 90, 0 15 4 0, 10, 11, 25 0, 62, 57, 0 16 5 1, 9, 11,12, 26 0, 37, 139, 33, 0 17 5 1, 5, 11, 12, 27 0, 10, 134, 108, 0 18 40, 6, 7, 28 0, 5, 95, 0 19 4 0, 1, 10, 29 0, 74, 7, 0 20 4 1, 4, 11, 300, 123, 35, 0 21 4 0, 8, 13, 31 0, 10, 36, 0 22 3 1, 2, 32 0, 130, 0 234 0, 3, 5, 33 0, 58, 102, 0 24 4 1, 2, 9, 34 0, 17, 49, 0 25 3 0, 5, 350, 2, 0 26 5 2, 7, 12, 13, 36 0, 103, 14, 132, 0 27 3 0, 6, 37 0, 1, 028 4 1, 2, 5, 38 0, 47, 99, 0 29 3 0, 4, 39 0, 80, 0 30 5 2, 5, 7, 9, 400, 72, 141, 124, 0 31 3 1, 13, 41 0, 50, 0 32 4 0, 5, 12, 42 0, 23, 28,0 33 4 2, 7, 10, 43 0, 26, 22, 0 34 4 0, 12, 13, 44 0, 65, 76, 0 35 4 1,5, 11, 45 0, 50, 96, 0 36 4 0, 2, 7, 46 0, 19, 107, 0 37 3 10, 13, 47 0,88, 0 38 4 1, 5, 11, 48 0, 74, 10, 0 39 4 0, 7, 12, 49 0, 119, 97, 0 404 2, 10, 13, 50 0, 114, 21, 0 41 4 1, 5, 11, 51 0, 105, 66, 0

TABLE 3b-6 (Corresponding to FIG. 3b-6) Row number Row Column index ofShift value of (row index) weight non-zero-element non-zero-element 0 80, 1, 2, 3, 6, 9, 0, 0, 0, 0, 0, 0, 0, 0 10, 11 1 10 0, 3, 4, 5, 6, 7,8, 173, 54, 0, 0, 168, 0, 9, 11, 12 0, 160, 0, 0 2 8 0, 1, 3, 4, 8, 10,97, 47, 149, 159, 32, 1, 12, 13 0, 0 3 10 1, 2, 4, 5, 6, 7, 8, 166, 21,118, 83, 125, 9, 10, 13 106, 58, 129, 0, 0 4 4 0, 1, 11, 14 0, 64, 76, 05 6 0, 1, 5, 7, 11, 15 0, 48, 21, 156, 173, 0 6 6 0, 5, 7, 9, 11, 16 0,147, 88, 169, 95, 0 7 6 1, 5, 7, 11, 13, 17 0, 103, 10, 140, 116, 0 8 40, 1, 12, 18 0, 1, 70, 0 9 5 1, 8, 10, 11, 19 0, 76, 71, 80, 0 10 5 0,1, 6, 7, 20 0, 127, 67, 29, 0 11 5 0, 7, 9, 13, 21 0, 109, 50, 19, 0 124 1, 3, 11, 22 0, 81, 138, 0 13 5 0, 1, 8, 13, 23 0, 47, 11, 161, 0 14 51, 6, 11, 13, 24 0, 1, 24, 93, 0 15 4 0, 10, 11, 25 0, 117, 134, 0 16 51, 9, 11, 12, 26 0, 58, 119, 50, 0 17 5 1, 5, 11, 12, 27 0, 56, 29, 77,0 18 4 0, 6, 7, 28 0, 42, 130, 0 19 4 0, 1, 10, 29 0, 164, 49, 0 20 4 1,4, 11, 30 0, 171, 164, 0 21 4 0, 8, 13, 31 0, 159, 125, 0 22 3 1, 2, 320, 79, 0 23 4 0, 3, 5, 33 0, 27, 140, 0 24 4 1, 2, 9, 34 0, 84, 13, 0 253 0, 5, 35 0, 94, 0 26 5 2, 7, 12, 13, 36 0, 14, 28, 151, 0 27 3 0, 6,37 0, 40, 0 28 4 1, 2, 5, 38 0, 67, 110, 0 29 3 0, 4, 39 0, 82, 0 30 52, 5, 7, 9, 40 0, 129, 87, 123, 0 31 3 1, 13, 41 0, 117, 0 32 4 0, 5,12, 42 0, 60, 41, 0 33 4 2, 7, 10, 43 0, 92, 103, 0 34 4 0, 12, 13, 440, 89, 83, 0 35 4 1, 5, 11, 45 0, 86, 49, 0 36 4 0, 2, 7, 46 0, 125,138, 0 37 3 10, 13, 47 0, 130, 0 38 4 1, 5, 11, 48 0, 63, 43, 0 39 4 0,7, 12, 49 0, 34, 21, 0 40 4 2, 10, 13, 50 0, 118, 86, 0 41 4 1, 5, 11,51 0, 65, 18, 0

TABLE 3b-7 (Corresponding to FIG. 3b-7) Row number Row Column index ofShift value of (row index) weight non-zero-element non-zero-element 0 80, 1, 2, 3, 6, 9, 0, 0, 0, 0, 0, 0, 0, 0 10, 11 1 10 0, 3, 4, 5, 6, 7,8, 113, 122, 0, 0, 23, 0, 9, 11, 12 0, 137, 0, 0 2 8 0, 1, 3, 4, 8, 10,103, 141, 93, 12, 154, 12, 13 1, 0, 0 3 10 1, 2, 4, 5, 6, 7, 8, 19, 163,39, 158, 173, 9, 10, 13 35, 83, 203, 0, 0 4 4 0, 1, 11, 14 0, 59, 200, 05 6 0, 1, 5, 7, 11, 15 0, 190, 135, 15, 111, 0 6 6 0, 5, 7, 9, 11, 16 0,23, 115, 163, 40, 0 7 6 1, 5, 7, 11, 13, 17 0, 78, 73, 46, 134, 0 8 4 0,1, 12, 18 0, 193, 54, 0 9 5 1, 8, 10, 11, 19 0, 166, 151, 19, 0 10 5 0,1, 6, 7, 20 0, 1, 72, 182, 0 11 5 0, 7, 9, 13, 21 0, 131, 174, 138, 0 124 1, 3, 11, 22 0, 174, 43, 0 13 5 0, 1, 8, 13, 23 0, 30, 167, 94, 0 14 51, 6, 11, 13, 24 0, 119, 203, 159, 0 15 4 0, 10, 11, 25 0, 141, 55, 0 165 1, 9, 11, 12, 26 0, 120, 27, 135, 0 17 5 1, 5, 11, 12, 27 0, 30, 109,23, 0 18 4 0, 6, 7, 28 0, 64, 55, 0 19 4 0, 1, 10, 29 0, 2, 79, 0 20 41, 4, 11, 30 0, 100, 41, 0 21 4 0, 8, 13, 31 0, 201, 130, 0 22 3 1, 2,32 0, 11, 0 23 4 0, 3, 5, 33 0, 101, 79, 0 24 4 1, 2, 9, 34 0, 88, 126,0 25 3 0, 5, 35 0, 116, 0 26 5 2, 7, 12, 13, 36 0, 52, 192, 112, 0 27 30, 6, 37 0, 188, 0 28 4 1, 2, 5, 38 0, 152, 148, 0 29 3 0, 4, 39 0, 87,0 30 5 2, 5, 7, 9, 40 0, 25, 66, 37, 0 31 3 1, 13, 41 0, 78, 0 32 4 0,5, 12, 42 0, 111, 172, 0 33 4 2, 7, 10, 43 0, 31, 119, 0 34 4 0, 12, 13,44 0, 38, 100, 0 35 4 1, 5, 11, 45 0, 201, 159, 0 36 4 0, 2, 7, 46 0,161, 129, 0 37 3 10, 13, 47 0, 99, 0 38 4 1, 5, 11, 48 0, 184, 140, 0 394 0, 7, 12, 49 0, 85, 110, 0 40 4 2, 10, 13, 50 0, 59, 36, 0 41 4 1, 5,11, 51 0, 118, 117, 0

TABLE 3b-8 (Corresponding to FIG. 3b-8) Row number Row Column index ofShift value of (row index) weight non-zero-element non-zero-element 0 80, 1, 2, 3, 6, 9, 0, 0, 0, 0, 0, 0, 0, 0 10, 11 1 10 0, 3, 4, 5, 6, 7,8, 63, 126, 0, 0, 229, 0, 9, 11, 12 0, 98, 0, 0 2 8 0, 1, 3, 4, 8, 10,100, 137, 42, 209, 50, 12, 13 1, 0, 0 3 10 1, 2, 4, 5, 6, 7, 8, 7, 83,3, 133, 207, 226, 9, 10, 13 32, 153, 0, 0 4 4 0, 1, 11, 14 0, 175, 53, 05 6 0, 1, 5, 7, 11, 15 0, 71, 139, 28, 138, 0 6 6 0, 5, 7, 9, 11, 16 0,90, 52, 64, 125, 0 7 6 1, 5, 7, 11, 13, 17 0, 209, 206, 237, 167, 0 8 40, 1, 12, 18 0, 139, 184, 0 9 5 1, 8, 10, 11, 19 0, 201, 126, 8, 0 10 50, 1, 6, 7, 20 0, 43, 145, 10, 0 11 5 0, 7, 9, 13, 21 0, 33, 61, 116, 012 4 1, 3, 11, 22 0, 236, 31, 0 13 5 0, 1, 8, 13, 23 0, 159, 141, 220, 014 5 1, 6, 11, 13, 24 0, 112, 32, 41, 0 15 4 0, 10, 11, 25 0, 11, 152, 016 5 1, 9, 11, 12, 26 0, 118, 25, 92, 0 17 5 1, 5, 11, 12, 27 0, 55,213, 218, 0 18 4 0, 6, 7, 28 0, 86, 53, 0 19 4 0, 1, 10, 29 0, 57, 143,0 20 4 1, 4, 11, 30 0, 228, 50, 0 21 4 0, 8, 13, 31 0, 58, 168, 0 22 31, 2, 32 0, 231, 0 23 4 0, 3, 5, 33 0, 74, 80, 0 24 4 1, 2, 9, 34 0,163, 144, 0 25 3 0, 5, 35 0, 198, 0 26 5 2, 7, 12, 13, 36 0, 20, 211,234, 0 27 3 0, 6, 37 0, 84, 0 28 4 1, 2, 5, 38 0, 155, 137, 0 29 3 0, 4,39 0, 195, 0 30 5 2, 5, 7, 9, 40 0, 227, 88, 91, 0 31 3 1, 13, 41 0, 21,0 32 4 0, 5, 12, 42 0, 37, 194, 0 33 4 2, 7, 10, 43 0, 132, 156, 0 34 40, 12, 13, 44 0, 55, 204, 0 35 4 1, 5, 11, 45 0, 195, 139, 0 36 4 0, 2,7, 46 0, 178, 15, 0 37 3 10, 13, 47 0, 206, 0 38 4 1, 5, 11, 48 0, 76,56, 0 39 4 0, 7, 12, 49 0, 197, 232, 0 40 4 2, 10, 13, 50 0, 14, 45, 041 4 1, 5, 11, 51 0, 189, 216, 0

It may be understood that FIG. 3a , FIGS. 3b -1 to 3 b-8, Table 2, andTables 3b-1 to 3b-8 are intended to help understanding the designs ofthe base graphs and the base matrices, and representation forms thereofare not limited thereto. Other possible variations may also be included.For example, for variations of Table 3b-1 and Table 3b-3 to Table 3b-8,reference may be made to a form of Table 3b-2A. Information aboutelements in columns, such as column 14 to column 51, that haverelatively definite structures and that are corresponding to a shiftvalue 0 may be selectively included in the table or may not be includedin the table, to save storage space.

In a design, for a part having a relatively definite structure in thebase graph or the base matrix, locations of non-zero-elements of thebase graph or the base matrix may be obtained through calculation basedon a row/column location, and the locations of the non-zero-elements maynot be stored. Using FIG. 3b -2 and Table 3b-2 as an example, locationsof column 14 to column 51 in the matrix shown in FIG. 3b -2 arerelatively definite, and shift values V_(i,j) are all 0. Locations ofnon-zero-elements can be calculated based on the knownnon-zero-elements. In Table 3b-2, information about column 14 to column51 may not be included, or information about some columns of column 14to column 51 may not be included. For example, nonzero elements incolumn 16 to column 51 and corresponding shift values of thenon-zero-elements may not be included. For example, the matrix shown inFIG. 3b -2 may alternatively be represented in Table 3b-2A.

TABLE 3b-2A Row number Row Column index of Shift value of (row index)weight non-zero-element non-zero-element 0 8 0, 1, 2, 3, 6, 9, 0, 0, 0,0, 0, 0, 0, 0 10, 11 1 10 0, 3, 4, 5, 6, 7, 8, 187, 56, 0, 0, 45, 0, 9,11, 12 0, 18, 0, 0 2 8 0, 1, 3, 4, 8, 10, 179, 171, 54, 158, 116, 12, 131, 0, 0 3 10 1, 2, 4, 5, 6, 7, 8, 106, 62, 52, 185, 80, 9, 10, 13 81,66, 163, 0, 0 4 3 0, 1, 11 0, 89, 43 5 5 0, 1, 5, 7, 11 0, 109, 191, 42,142 6 5 0, 5, 7, 9, 11 0, 163, 112, 100, 131 7 5 1, 5, 7, 11, 13 0, 60,78, 92, 183 8 3 0, 1, 12 0, 123, 58 9 4 1, 8, 10, 11 0, 180, 55, 49 10 40, 1, 6, 7 0, 134, 184, 158 11 4 0, 7, 9, 13 0, 153, 164, 189 12 3 1, 3,11 0, 167, 154 13 4 0, 1, 8, 13 0, 187, 166, 67 14 4 1, 6, 11, 13 0, 29,67, 145 15 3 0, 10, 11 0, 21, 16 16 4 1, 9, 11, 12 0, 122, 113, 98 17 41, 5, 11, 12 0, 99, 112, 70 18 3 0, 6, 7 0, 135, 164 19 3 0, 1, 10 0,94, 90 20 3 1, 4, 11 0, 173, 59 21 3 0, 8, 13 0, 8, 143 22 2 1, 2 0, 4223 3 0, 3, 5 0, 190, 72 24 3 1, 2, 9 0, 73, 111 25 2 0, 5 0, 188 26 4 2,7, 12, 13 0, 0, 1, 113 27 2 0, 6 0, 185 28 3 1, 2, 5 0, 41, 89 29 2 0, 40, 36 30 4 2, 5, 7, 9 0, 141, 35, 124 31 2 1, 13 0, 152 32 3 0, 5, 12 0,145, 117 33 3 2, 7, 10 0, 68, 176 34 3 0, 12, 13 0, 92, 75 35 3 1, 5, 110, 189, 18 36 3 0, 2, 7 0, 140, 179 37 2 10, 13 0, 19 38 3 1, 5, 11 0,44, 3 39 3 0, 7, 12 0, 111, 167 40 3 2, 10, 13 0, 27, 92 41 3 1, 5, 110, 158, 156

For another example, using FIG. 3b -2 as an example, shift valuesV_(i,j) in row 0 are also 0, and information about row 0 may not bestored, but is obtained through calculation.

In an implementation, the parameter “row weight” in Table 2, Tables 3b-1to 3b-8, and Table 3b-2A may alternatively be omitted. A quantity ofnon-zero-elements in a row may be learned based on a column in which thenon-zero-elements in the row are located. Therefore, the row weight isalso learned.

In an implementation, parameter values in the “column in which anon-zero-element is located” in Table 2, Table 3b-1 to Table 3b-8, andTable 3b-2A may not be arranged in ascending order, provided that theparameter values are indexed to columns in which non-zero-elements arelocated. Moreover, parameter values in the “shift value of anon-zero-element” in Table 2 and Table 3b-1 to Table 3b-8 may not bearranged in a column order, provided that the parameter values in the“shift value of non-zero-element” are in a one-to-one correspondencewith the parameter values in the “Column index of non-zero-element”.

In an implementation, the foregoing different base matrices may becombined into one or more tables for representation. For example,non-zero-elements corresponding to different base matrices have a samelocation and a same row number, but have different shift values V_(i,j).Therefore, a plurality of base matrices may be represented by using onetable by listing row numbers, columns index in which non-zero-elementsare located, and shift values of a plurality of groups ofnon-zero-elements. For example, shift values of two groups ofnon-zero-elements may be listed in different columns, and are indicatedby using indexes.

In an implementation, the base graph may be used to indicate locationsof non-zero-elements. The parameter “Column index of non-zero-element”in the foregoing tables may alternatively be optional.

In an implementation, the matrices shown in FIG. 3a and FIGS. 3b -1 to 3b-8 may alternatively be represented by using column numbers (columnindexes), rows in which non-zero-elements are located, and shift valuesof the non-zero-elements. Optionally, column weight may be included.

In another implementation, 1 and 0 in each row or each column in thebase graph or the base matrix may be considered as binary numerals, andstoring the binary numerals in decimal numerals or hexadecimal numeralscan save storage space. Using any foregoing base graph or base matrix asan example, locations of non-zero-elements in first 14 columns or first17 columns may be stored by using hexadecimal numerals. For example, iffirst 14 columns in row 0 are 11110010011100, locations of thenon-zero-elements in row 0 may be recorded as 0xF2 and 0x70. That is,every 8 columns form a hexadecimal numeral. For last two columns, acorresponding hexadecimal numerals may be obtained by filling zeroes toreach an integer multiple of 8 bits. Alternatively, a correspondinghexadecimal number may be obtained by filling zeroes in first twocolumns to reach an integer multiple of 8 bits. The same is true ofother rows and details are not described herein.

FIG. 5 shows a flowchart of a data processing process. The dataprocessing process may be implemented by using a communicationapparatus. The communication apparatus may be a base station, aterminal, or other entity such as a communication chip, or an encoder/adecoder, etc.

Block 501: Obtain an input sequence. In an implementation, an inputsequence for encoding may be an information bit sequence, a filledinformation bit sequence, or a sequence obtained by adding a CRC bitsequence to an information bit sequence. Sometimes the information bitsequence is also referred to as a code block, for example, may be anoutput sequence obtained by performing code block segmentation on atransport block. In an implementation, an input sequence for decodingmay be a soft value sequence of an LDPC code.

Block 502: Encode/decode the input sequence based on an LDPC matrix. Abase matrix of the LDPC matrix may be any base matrix shown in theforegoing examples.

In an implementation, the LDPC matrix may be obtained based on a liftingfactor Z and the base matrix.

In an implementation, parameters related to the LDPC matrix may bestored. The parameters include one or more of the following:

(a) Parameters used to obtain any base matrix listed in the foregoingimplementations. The base matrix may be obtained based on theparameters. For example, the parameters may be one or more of thefollowing: row index, row weight, column index, column weight; locationsof non-zero-elements (such as row indexes of the non-zero-elements, orcolumn indexes of the non-zero-elements), shift values in the basematrix, shift values of non-zero-elements and corresponding locations ofthe non-zero-elements, a compensation value, a lifting factor Z, a basegraph, a code rate, and the like;

(b) A base matrix, which is one of any base matrices listed in theforegoing implementations;

(c) A compensation matrix H_(s), obtained by compensating at least onecolumn to the base matrix;

(d) A matrix obtained by lifting (expanding) the base matrix or thecompensation matrix H_(s) of the base matrix;

(e) A base matrix obtained by performing a row/column transformation onany base matrix or compensation matrix H_(s) of the base matrix listedin the foregoing implementations;

(f) A matrix obtained by lifting a row/column transformed base matrix ora row/column transformed compensation matrix H_(s) of the base matrix;and

(g) A base matrix obtained by performing a shortening or puncturingoperation on any base matrix or compensation matrix H_(s) of the basematrix listed in the foregoing implementations.

In a possible implementation, encoding/decoding an input sequence basedon a low density parity check (LDPC) matrix may be performed in anencoding/decoding process in one or more of the following manners:

i. Obtaining a base matrix based on some or all of the parameters listedin the forgoing item (a), and then:

encoding/decoding information based on the obtained base matrix; or

performing a row/column transformation on the obtained base matrix, andencoding/decoding information based on the row/column transformed basematrix; or

encoding/decoding information based on a compensation matrix H_(s) ofthe obtained base matrix; or

encoding/decoding information based on a matrix, which is obtained byperforming a row/column transformation on a compensation matrix H_(s) ofthe base matrix. Alternatively, the encoding/decoding information basedon the base matrix or the compensation matrix H_(s) may further include:encoding/decoding information based on a base matrix lifted from thebase matrix or the compensation matrix H_(s) of the base matrix; or

encoding/decoding information based on a matrix obtained by performing ashortening or puncturing operation on the base matrix or thecompensation matrix H_(s).

ii. Encoding/decoding information based on a matrix stored according tothe forgoing item (b), (c), (d), or (e). The matrix may be a stored basematrix, a compensation matrix H_(s) of the base matrix, a matrixobtained by performing a row/column transformation on the base matrix,or a matrix obtained by performing a row/column transformation on thecompensation matrix H_(s). Alternatively, a row/column transformation isperformed on the stored base matrix, and encoding/decoding is performedbased on a matrix obtained by performing the row/column transformation.Herein, optionally, the encoding/decoding based on the base matrix orthe compensation matrix H_(s) may further include: performingencoding/decoding based on a spreading matrix of the base matrix or aspreading matrix of the compensation matrix H_(s); or performingencoding/decoding based on a matrix obtained after performing ashortening or puncturing operation on the base matrix or thecompensation matrix H_(s).

iii. Encoding/decoding information based on a matrix described in theforgoing (d), (f), or (g).

Block 503: Output an encoded/decoded bit sequence. In a design, an inputsequence c={c₀, c₁, c₂, . . . c_(K−1)} may be encoded to obtain anoutput sequence d={d₀, d₁, d₂, . . . , d_(N−1)}, where K and N areintegers greater than 0. The output sequence d includes K₀ bits in theinput sequence c and parity bits in a parity check sequence w, where K₀is an integer, and 0<K₀≤K. The parity sequence w and the input sequencec satisfy a formula

${{H \times \begin{bmatrix}c^{T} \\w^{T}\end{bmatrix}} = 0^{T}},$

where c^(T)=[c₀, c₁, c₂, . . . , c_(K−1)]^(T) is a transposed vector ofa vector formed by bits in the input sequence c, w^(T)=[w₀, w₁, w₂, . .. w_(N−K0−1)]^(T) is a transposed vector of a vector formed by bits inthe parity sequence w; 0^(T) is a column vector, and values of allelements in 0^(T) are 0; and H is a low density parity check (LDPC)matrix. A base graph of H includes H_(BG) and H_(BG,EXT):

${H_{{BG},{EXT}} = \begin{bmatrix}0_{m_{c} \times n_{c}} \\I_{n_{c} \times n_{c}}\end{bmatrix}},$

where 0_(m) _(c) _(×n) _(c) represents an all zero matrix of sizem_(c)×n_(c), and I_(n) _(c) _(×n) _(c) represents an identity matrix ofsize n_(c)×n_(c); and H_(BG) includes columns corresponding to K_(b)columns of information bits in H_(BG2) and column 10 to column10+m_(A)−1 in H_(BG2), where a quantity of columns in H_(BG2) is10+m_(A), 4≤m_(A)≤7, where K_(b)∈{6, 8, 9, 10}. For m_(c)=7, and0≤n_(c)≤35, a quantity of columns in H_(BG2) is equal to 17; or form_(c)=6, and 0≤n_(c)≤36, a quantity of columns in H_(BG2) is equal to16; or for m_(c)=5, and 0≤n_(c)≤37, a quantity of columns in H_(BG2) isequal to 15; or for m_(c)=4, and 0≤n_(c)≤38, a quantity of columns inH_(BG2) is equal to 14.

FIG. 6 shows a flowchart of a data processing process, which may beapplied to block 502 in FIG. 5.

Block 601: Obtain a lifting factor Z. In a possible design, filling maybe performed on an information bit sequence to obtain an input sequence.A length of the input sequence is K=K_(b)·Z, and Z=K/K_(b). In anotherpossible design, bits that need to be punctured or shortened in aninformation bit sequence may be filled. In other words, filling bits areused to replace the bits that need to be punctured or shortened, so thatafter encoding, the filling bits can be identified and are not sent. Forexample, a null value, a value 0, a value agreed in a system, or apredefined value may be used as a value of a filling bit. In a design,the bits that need to be punctured are punctured without filing. Fillingbits are filled after the information bit sequence.

In an implementation, the lifting factor Z may be determined based onthe length K of the input sequence. For example, a minimum Z₀ that meetsK_(b)·Z₀≥K may be determined from a plurality of lifting factors in asupported lifting factor set and may be used as a value of the liftingfactor Z. In a possible design, K_(b) may be a quantity of columns ofinformation bits in a base matrix of an LDPC code. For a base graph inFIG. 3a , a quantity of columns of information bits is K_(bmax)=10. Itis assumed that a lifting factor set supported by the base graph in FIG.3a is {24, 26, 28, 30, 32, 36, 40, 44, 48, 52, 56, 60, 64, 72, 80, 88,96, 104, 112, 120, 128, 144, 160, 176, 192, 208, 224, 240, 256, 288,320, 352, 384}. If the length of the input sequence is K=529 bits, Z isequal to 26. If the length of the input sequence is K=5000 bits, Z isequal to 240. It should be noted that this is merely an example herein,which is not limited thereto.

For another example, a value of K_(b) may vary with the value of K, butdoes not exceed the quantity of columns of information bits in the basematrix of the LDPC code. For example, different thresholds may be setfor K_(b).

In a design, it should be noted that thresholds 640, 560, and 192 hereinare merely examples. Alternatively, another value may be designeddepending on a system design requirement.

if (K>640), K_(b)=10; else if (K>560), K_(b)=9; else if (K>192),K_(b)=8; else K_(b)=6; end

The lifting factor Z may be determined by a communication apparatusbased on the length K of the input sequence, or may be obtained by thecommunication apparatus from another entity (for example, a processor).

Block 602: Obtain an LDPC matrix based on the lifting factor and a basematrix. The base matrix is any base matrix listed in the foregoingimplementations, a compensation matrix obtained by compensating at leastone column in any base matrix listed above, or a base matrix obtainedafter transformation is performed on a row order, a column order, or arow order and a column order of any base matrix listed above or acompensation matrix. A base graph of the base matrix includes at least asubmatrix A and a submatrix B. Optionally, the base graph may furtherinclude a submatrix C, a submatrix D, and a submatrix E. Fordescriptions of the submatrices, reference may be made to thedescriptions in the foregoing embodiments. Details are not describedherein again. The base matrix may be obtained based on the base graphand a shift value, may be any stored base matrix listed in the foregoingimplementations, or may be obtained through variation of any base matrixlisted in the foregoing implementations.

In a possible implementation, the corresponding base matrix isdetermined based on the lifting factor Z, and the base matrix ispermutated based on the lifting factor Z to obtain the LDPC matrix.

In an implementation, the LDPC matrix H may be obtained based on acorrespondence between the lifting factor and the base matrix. Forexample, the corresponding base matrix is determined based on thelifting factor Z obtained in block 601.

For example, if Z is equal to 26, and a is equal to 13, the base matrixmay include row 0 to row 6 and column 0 to column 16 in a matrix shownin FIG. 3b -7, or the base matrix includes row 0 to row 6 and somecolumns of column 0 to column 16 in a matrix shown in FIG. 3b -7.Further, alternatively, the base matrix further includes row 0 to rowm−1 and column 0 to column n−1 in a matrix, where 7≤m≤42, m is aninteger, 17≤n≤52, and n is an integer; or the base matrix includes row 0to row m−1 and column 0 to column n−1 in a matrix shown in FIG. 3b -7,where 7≤m≤42, m is an integer, 17≤n≤52, and n is an integer. The basematrix is permutated based on the lifting factor Z to obtain the LDPCmatrix. It should be noted that herein, Z=26, a=13, and the matrix shownin FIG. 3b -7 are only used as an example for description. This ismerely an example herein, and the present application is not limitedthereto. It may be understood that different lifting factors lead todifferent base matrices.

In a possible implementation, the correspondence between the liftingfactor and the base matrix may be listed in Table 4, and a base matrixindex corresponding to the lifting factor is determined based on Table4. In a possible design, PCM1 may be the matrix shown in FIG. 3b -1,PCM2 may be the matrix shown in FIG. 3b -2, PCM3 may be the matrix shownin FIG. 3b -3, PCM4 may be the matrix shown in FIG. 3b -4, PCM5 may bethe matrix shown in FIG. 3b -5, PCM6 may be the matrix shown in FIG. 3b-6, PCM7 may be the matrix shown in FIG. 3b -7, and PCM8 may be thematrix shown in FIG. 3b -8. This is merely an example herein, which isnot limited thereto.

TABLE 4 Base matrix index Lifting factor Z PCM1 2 4 8 16 32 64 128 256PCM2 3 6 12 24 48 96 192 384 PCM3 5 10 20 40 80 160 320 PCM4 7 14 28 56112 224 PCM5 9 18 36 72 144 288 PCM6 11 22 44 88 176 352 PCM7 13 26 52104 208 PCM8 15 30 60 120 240

In another design, the following manner may alternatively be used:

TABLE 4A Base matrix index Lifting factor Z PCM1 2 4 8 16 32 64 128 256PCM2 3 6 12 24 48 96 192 PCM3 5 10 20 40 80 160 PCM4 7 14 28 56 112 224PCM5 9 18 36 72 144 PCM6 11 22 44 88 176 PCM7 13 26 52 104 208 PCM8 1530 60 120 240

Further, in a possible design, for the lifting factor Z, an elementP_(i,j) in row i and column j in the base matrix may satisfy thefollowing relationship:

$P_{i,j} = \left\{ \begin{matrix}{- 1} & {V_{i,j} = {- 1}} \\{{mod}\left( {V_{i,j},Z} \right)} & {V_{i,j} \geq 0}\end{matrix} \right.$

where V_(i,j) may be a shift value of an element in row i and column jin a base matrix for a set to which the lifting factor Z belongs, or ashift value of a non-zero-element in row i and column j in a base matrixcorresponding to a maximum lifting factor in a set which the liftingfactor Z belongs.

For example, Z is equal to 13. An element P_(i,j) in row i and column jin a base matrix corresponding to Z satisfies:

$P_{i,j} = \left\{ \begin{matrix}{- 1} & {V_{i,j} = {- 1}} \\{{mod}\left( {V_{i,j},Z} \right)} & {V_{i,j} \geq 0}\end{matrix} \right.$

where V_(i,j) is a shift value of a non-zero-element in row i and columnj in PCM7, that is, a matrix shown in FIG. 3b -7. For Z=13, performmodulo operation of V_(i,j) modulo 13, where V_(i,j) is a shift value ofthe non-zero-element in row i and column j in the matrix shown in FIG.3b -7. It should be noted that this is merely an example herein, and thepresent application is not limited thereto.

Block 603: Encode/decode the input sequence based on the LDPC matrix.

In an implementation, the input sequence for encoding may be aninformation bit sequence. In another implementation, the input sequencefor decoding may be a soft value sequence of the LDPC code, andreference may be made to the related descriptions in FIG. 5. Whenencoding/decoding the input sequence, the LDPC matrix H may be obtainedby lifting the base matrix based on Z. For each non-zero-element P_(i,j)in the base matrix, determine a circular permutation matrix h_(i,j) ofsize Z×Z, where h_(i,j) is a circular permutation matrix obtained bycircularly shifting an identity matrix for P_(i,j) times. Anon-zero-element P_(i,j) is replaced with h_(i,j), and zero-elements inthe base matrix H_(B) are replaced with an all zero matrix of size Z×Z,so as to obtain the parity check matrix H.

In a possible implementation, the base matrix of the LDPC code may bestored in a memory. The communication apparatus obtains the LDPC matrixcorresponding to the lifting factor Z, to encode/decode the inputsequence.

In a possible implementation, because there are a plurality of basematrices of the LDPC code, relatively large storage space is occupied ifthe base matrices are stored based on a matrix structure. Alternatively,the base graph of the LDPC code may be stored in the memory, and shiftvalues of non-zero-elements in each base matrix are stored row by row orcolumn by column, and then the LDPC matrix is obtained based on the basegraph and a shift value in the base matrix associated with the liftingfactor Z.

In a possible implementation, the shift values of the non-zero-elementsin each base matrix may be stored according to Table 2 and Table 3b-1 toTable 3b-8. As a parameter of the LDPC matrix, Parameter “row weight” ofthe LDPC matrix is optional. In other words, parameter “row weight” maybe or may not be stored. A quantity of non-zero-elements in a row islearned based on a column in which the non-zero-elements in the row arelocated. Therefore, the row weight is also learned. In a possibleimplementation, parameter values in the “column index ofnon-zero-element” in Table 2 and Table 3b-1 to Table 3b-8 mayalternatively not be arranged in ascending order, as long as theparameter values are indexed to column index in which thenon-zero-elements are located. Moreover, parameter values in the “shiftvalue of non-zero-element” in Table 2 and Table 3b-1 to Table 3b-8 mayalternatively not be arranged in a column index order, as long as theparameter values in the “shift value of non-zero-element” are in aone-to-one correspondence with the parameter values in the “column indexof non-zero-element” and the communication apparatus can learn a shiftvalue of anon-zero-element in which row and which column. For example,in an implementation, the shift value of non-zero-elements may belearned according to the parameter values of column index, columnweight, and row index of non-zero-element, or row index of zero-element.This is similar to the form in Table 2 and Table 3b-1 to Table 3b-8, anddetails are not described herein again.

In a possible implementation, related parameters of the LDPC matrix maybe stored with reference to related descriptions in FIG. 5.

In a possible implementation, when the related parameters of the LDPCmatrix are stored, not all rows in the matrices in FIG. 3a and FIGS. 3b-1 to 3 b-8 or not all rows in the matrices in Table 2 and Table 3b-1 toTable 3b-8 are stored, and parameters indicated by corresponding rows inthe tables may be stored based on rows included in the base matrix. Forexample, a matrix constituted by rows and columns included in the basematrix of the LDPC matrix described in the foregoing embodiments orrelated parameters of the matrix constituted by the rows and the columnsmay be stored.

For example, for row 0 to row 6 and column 0 to column 16 in any matrixin FIGS. 3b -1 to 3 b-8, a matrix constituted by row 0 to row 6 andcolumn 0 to column 16 and/or related parameters of a matrix constitutedby row 0 to row 6 and column 0 to column 16 may be stored. For details,reference may be made to the parameters listed in Table 3b-1 to Table3b-8 and some of the foregoing descriptions.

For row 0 to row m−1 and column 0 to column n−1 in any matrix in FIGS.3b -1 to 3 b-8, where 7≤m≤42, m is an integer, 17≤n≤52, and n is aninteger, a matrix constituted by row 0 to row m−1 and column 0 to columnn−1 and/or related parameters of the matrix constituted by row 0 to rowm−1 and column 0 to column n−1 may be stored. For details, reference maybe made to the parameters listed in Table 3b-1 to Table 3b-8 and some ofthe foregoing descriptions.

In a possible implementation, a compensation value Offset_(s) may beadded to or subtracted from each shift value that is greater than orequal to 0 in at least one locations indicated by “column index ofnon-zero-element” in any one of Table 2 and Table 3b-1 to Table 3b-8. Itshould be noted that this is merely an example herein, which is notlimited thereto.

Using FIG. 1 as an example, in an implementation, after the base matrixH_(B) is determined, first, parity bits corresponding to column 10 tocolumn 15 may be obtained based on the input sequence and row 0 to row 3and column 0 to column 9 in the base matrix, that is, H_(core-dual).Next, parity bits corresponding to column 16, that is, a column withcolumn weight of 1, are obtained based on the input sequence and paritybits corresponding to H_(core-dual). Then, parity bits corresponding tothe submatrix E are obtained by encoding the submatrix D based on theinput sequence and the parity bits corresponding to column 10 to column16 in order to complete encoding. For an encoding process of the LDPCcode, reference may be made to the descriptions in the foregoingimplementations. Details are not described herein again.

In a design, in the foregoing part 502 and part 603, when the inputsequence is encoded/decoded based on the LDPC matrix, the input sequencemay be encoded by using the LDPC matrix H corresponding to the liftingfactor Z.

In a possible implementation, LDPC encoding may be implemented in thefollowing manner:

(1) The to-be-encoded input sequence is represented as c={c₀, c₁, c₂, .. . , c_(K−1)}, the length of the input sequence c is K, and an outputsequence obtained by encoding the input sequence c by an encoder isrepresented as d={d₀, d₁, d₂, . . . , d_(N−1)}, where K is an integergreater than 0, K may be an integer multiple of the lifting factor Z,the lifting factor of the input sequence c may be represented as Z orZ_(c), and the subscript c indicates that the lifting factor isassociated to the input sequence c. Optionally, other parameters in thisimplementation may be provided with or not provided with a subscriptindex. This does not affect an essential meaning of the parameter. Aperson skilled in the art may understand the meaning thereof, whereN=50Z or N=(40+K_(b))·Z. The length of the input sequence c is K, thelength of the output sequence d is N, and the output sequence of N bitsmay include K₀ bits in the input sequence c and N−K₀ parity bits in aparity sequence w, where K₀ is an integer, and 0<K₀≤K. The paritysequence w may be represented as w={w₀, w₁, w₂, . . . , w_(N−K0−1)}, anda length of the parity sequence w is N−K₀. In a design, if the LDPCmatrix H includes p built-in puncture column(s), where p is an integergreater than or equal to 0, and the p built-in puncture column(s)does/do not participate in encoding, for example, p=2, a length of theparity sequence w is N+2Z_(c)−K, and the parity sequence w may berepresented as w={w₀, w₁, w₂, . . . , w_(N+2Zc−K−1)}. If the p built-inpuncture column(s) participate in encoding, the length of the paritysequence w is N−K, and the parity sequence w may be represented as {w₀,w₁, w₂, . . . , w_(N−K−1)}.

For a value of K_(b), reference may be made to the foregoing design. Forexample:

if (K>640), K_(b)=10; else if (K>560), K_(b)=9; else if (K>192),K_(b)=8; else K_(b)=6; end

(2) A PCM index or a lifting factor set index corresponding to thelength K of a bit segment is determined based on Z_(c)=K/K_(b). Forexample, the lifting factor Z_(c) may be determined with reference toTable 1 and Table 2.

(3) Values are assigned to first K−2Z_(c) bits in the encoded bitsequence d={d₀, d₁, d₂, . . . , d_(N−1)}. Herein, first 2Z_(c) fillingbits in the to-be-encoded bit segment need to be skipped, and that theto-be-encoded bit segment may include a filling bit needs to beconsidered.

In an implementation, value assignment may be performed in the followingmanner:

for k=2Z_(c) to k−1, if c_(k)≠<NULL> d_(k-2Zc)=c_(k); else c_(k)=0;d_(k-2Zc)=<NULL>; end if end for

where k is an index value, k is an integer, <NULL> represents a fillingbit, and a value thereof may be 0 or other predetermined value.Optionally, the filling bit may not to be sent.

(4) The parity bits w are generated, so that the parity bits satisfy thefollowing formula:

$\begin{matrix}{{H \times \begin{bmatrix}c \\w\end{bmatrix}} = 0} & (1)\end{matrix}$

In the formula (1), c=[c₀, c₁, . . . , c_(K−1)]^(T), where 0 representsa column vector, and values of all elements in 0 are zero. The matrix Hrepresents an LDPC check matrix, and may be divided into two parts H₁and H₂ for representation, for example, H=[H₁ H₂]. c=[c₀, c₁, c₂, . . ., c_(K−1)]^(T) is a transposed vector of a vector formed by bits in theinput sequence. The parity bits w in the formula (1) are a transposedvector of a vector formed by bits in the parity sequence w. For example,for N+2Z_(c)−K parity bits, w=[W₀, W₁, W₂, . . . , W_(N+2Zc−K−1)]^(T)are a transposed vector of a vector formed by bits in a parity sequence{W₀, W₁, W₂, . . . , W_(N+2Zc−K−1)}. For another example, for N−K−1parity bits, w=[W₀, W₁, W₂, . . . , W_(N−K−1)]^(T) is a transposedvector of a vector formed by bits in a parity sequence {W₀, W₁, W₂, . .. , W_(N−K−1)}. H in the formula (1) is any one of LDPC matrix listed inthe foregoing embodiments.

In an implementation, H may be obtained based on any base graph listedin the foregoing embodiments and a Z_(c)×Z_(c) spreading matrix. Eachzero-element in the base graph is replaced with an all zero matrix ofsize Z_(c)×Z_(c). An element whose value is 1 (non-zero-element) in thebase graph is replaced with a Z*Z circulant permutation matrixI(P_(i,j)) corresponding to a shift value P_(i,j) of the element, wherei and j represent a row index and a column index of the element. Thecircular permutation matrix I(P_(i,j)) is obtained by circularlyshifting the matrix of size Z_(c)×Z_(c) to the right or to the leftP_(i,j) times, where P_(i,j)=mod(V_(i,j), Z_(c)), and V_(i,j) is a shiftvalue that is in the base matrix and that is corresponding to anon-zero-element in the base graph.

In an implementation, H₁ may be parts A, B, and D of the base graph orthe base matrix listed in the foregoing embodiments, that is, row 10 torow 41 and column 0 to column 16 in FIG. 3a and FIGS. 3b -1 to 3 b-8.

In an implementation, H₁ may be some rows and some columns in the partsA, B, and D of the base graph or the base matrix listed in the foregoingembodiments, for example, row 0 to row 41 and column 0 to column 13, orrow 0 to row 41 and column 0 to column 14, or row 0 to row 41 and column0 to column 15, or row 1 to row 41 and column 0 to column 13.

In an implementation, H₁ may alternatively be m rows and n columns inthe base graph or the base matrix listed in the foregoing embodiments,for example, m=7 and n=35, or m=4 and n=38, or m=5 and n=37, or m=6 andn=36.

In an implementation, based on a value of K_(b), an input sequencelength of the encoder is K_(b)×Z. If K_(b)<9, columns {K_(b), K_(b+1), .. . ,9} in the matrix H₁ are removed, and then encoding is performed.

In an implementation, the matrix H may include M rows and (N+p·Z)columns or M rows and N columns, and a size of the base matrix of H ism=M/Z rows, and n=(N+p·Z)/Z columns or n=N/Z columns.

In an implementation, H₂ may be represented as

${H_{2} = \begin{bmatrix}0_{m \times n} \\I_{n \times n}\end{bmatrix}},$

where 0_(m×n) represents an m×n all zero matrix (m rows and n columns),for example, may have 7 rows and 35 columns, or 4 rows and 38 columns,or 5 rows and 37 columns, or 6 rows and 36 columns, and I_(n×n)represents an n×n (n rows and n columns) matrix, for example, may have35 rows and 35 columns, or 36 rows and 36 columns, or 37 rows and 37columns, or 38 rows and 38 columns.

In an implementation, when the matrix H is used for encoding, encodingmay be performed based on any one of the foregoing described base graphsor base matrices, for example, may be performed based on a matrix of row0 to row 41 and column 0 to column 16 in any one of the matrices in FIG.3a or FIGS. 3b -1 to 3 b-8, or may be performed based on a matrix of row0 to row 41 and column 0 to column 13 in any one of the matrices in FIG.3a or FIGS. 3b -1 to 3 b-8.

In a design, for K_(b)∈{6,8,9}, the matrix H may be a matrix obtainedafter columns {K_(b), K_(b)+1, . . . ,9} are removed from any basismatrix or basis matrix described above; for K_(b)=10, the matrix H maybe any base graph or base matrix described above.

The shift value V_(i,j) in the matrix H may be obtained based on inFIGS. 3b -1 to 3 b-8, or Table 3b-1 to Table 3b-8 and Table 3b-2A, orany manner described above. Based on an index of the check matrix, whichis sometimes considered as a lifting factor set index, a correspondingcheck matrix may be determined, thereby a corresponding shift valueV_(i,j) are obtained.

In a design, H includes p built-in puncture column(s), where p is aninteger greater than or equal to 0, and the p built-in puncturecolumn(s) does/do not participate in encoding. For example, p is equalto 2, and a length of the parity sequence w is N+2Z_(c)−K. If the pbuilt-in puncture columns participate in encoding, a length of theparity sequence w is N−K.

In a design, 0_(m×n) may be a submatrix C, the submatrix C plus a lastcolumn in the submatrix B, a submatrix C plus last two columns of thesubmatrix B, or a submatrix C plus last three columns of the submatrix Bin the foregoing embodiments.

I_(n×n) may be the submatrix E, the submatrix E plus a last column ineach of the submatrix B and the submatrix D, the submatrix E plus lasttwo columns of each of the submatrix B and the submatrix D, or thesubmatrix E plus last three columns of each of the submatrix B and thesubmatrix D in the foregoing embodiments.

(5) Optionally, for k=K to N+2Z_(c)−1, d_(k−2Zc)=w_(k−K).

In the foregoing implementations, the encoder may perform encoding andoutputting in a plurality of manners. Any one of the base graphs or thebase matrices shown in FIG. 3a and FIGS. 3b -1 to 3 b-8 listed in theforegoing embodiments is used as an example for description below. Thebase graph has a maximum of 42 rows and a maximum of 52 columns,including two built-in puncture columns. For ease of description, in thepresent application, sometimes a base graph/base matrix with a maximumquantity of rows and a maximum quantity of columns is referred to as acomplete base graph or base matrix. A base graph/base matrix obtained byremoving the two built-in puncture columns from the complete basegraph/base matrix is referred to as a complete base graph/base matrixthat includes no built-in puncture column.

Manner 1

Encoding is performed based on the complete base graph/base matrix orthe complete base graph/base matrix that includes no built-in puncturecolumn, so as to obtain as many parity bits as possible. In this case, mis equal to 42. If the built-in puncture columns participate inencoding, n is equal to 52, that is, row 0 to row 41 and column 0 tocolumn 51 in any one of the matrices in FIG. 3a and FIGS. 3b -1 to 3b-8. If the built-in puncture columns does not participate in encoding,n is equal to 51, that is, row 0 to row 41 and column 2 to column 51.Correspondingly, for the LDPC matrix H, M is equal to 41Z, and N isequal to 52Z or 51Z. In a subsequent processing process, informationbits and parity bits that need to be sent may be determined from theoutput sequence generated by the encoder.

Manner 2

Encoding is performed based on some rows and columns of the completebase graph. A row and a column may be selected, from the complete basegraph or the complete base graph that includes no built-in puncturecolumn and based on a code rate that needs to be used for sending, theinformation bits and the parity bits, or the like, for encoding. Forexample, the code rate is ⅔, and m is equal to 7. If the built-inpuncture columns participate in encoding, n is equal to 17. To bespecific, encoding is performed based on some of row 0 to row 6 andcolumn 0 to column 16 in any matrix in FIG. 3a and FIGS. 3b -1 to 3 b-8.If the built-in puncture columns participate in encoding, n is equal to15, that is, a row 0 to a row 6 and a column 2 to a column 16 in anymatrix in FIG. 3a and FIGS. 3b -1 to 3 b-8.

In a possible design, column 14 to column 51 in any matrix in FIG. 3aand FIGS. 3b -1 to 3 b-8 listed above are columns with column weight of1, and one or more of the columns with column weight of 1 in the corematrix may be punctured. One or more corresponding columns in the corematrix may be encoded based on some of row 0 to row 6 and column 0 tocolumn 15 in any matrix in FIG. 3a and FIGS. 3b -1 to 3 b-8, where forexample, m is 6, n is 16, and the built-in puncture columns participatein encoding. In an implementation, the built-in puncture columns mayalternatively not participate in encoding, so that a higher code ratecan be obtained.

It should be noted that the foregoing describes the principle of thematrix H. The solution provided in this embodiment of the presentapplication may be implemented based on various transformations of thematrix H, provided that the generated parity bits satisfy the formula(1).

A possible implementation is that Quasi-Cycle (QC) expansion isperformed on the matrix H before being used. In another possibleimplementation, in a use process of the matrix H, QC expansion isperformed on a part corresponding to current to-be-processed elements.

A possible implementation is that (calculating a shift value), thematrix H is not lifted in a use process, but a method for an expandableequivalence formula is used to calculate a connection relationshipbetween rows and columns of the matrix.

A possible implementation is that the matrix H may not be lifted. In anencoding process, for each to-be-processed element, a shifting operationis performed on a to-be-encoded bit segment corresponding to the elementbased on a shift value of the element. Then, an encoding operation isperformed on all bit segments on which the shifting operation isperformed.

In a possible implementation, the base matrix may be obtained bypredefining a base matrix PCM or defining a base matrix PCM by a system,without using the base graph. For example, the LDPC matrix may beobtained based on the base matrices provided in FIGS. 3b -1 to 3 b-8, orthe LDPC matrix may be obtained based on the corresponding Table 3b-1 toTable 3b-8.

In an implementation process, a transmitting end or a receiving end maystore a complete matrix, that is, all of A, B, C, D, and E.Alternatively, a complete matrix may not be stored, to save storagespace. For example, encoding/decoding can be implemented by storing onlya part of the complete matrix or parameters corresponding to the matrixneeds to be stored. Compared with a method in which a complete matrix isstored, storing only a part of a matrix can reduce overheads of astorage device in a codec. For details, reference may be made to thedescriptions in the foregoing embodiments.

For example, in an implementation, parts A, B, and D in the matrix arestored, or parts A, B, and D do not include a part with column weightof 1. In an actual encoding/decoding process, values of the parts C andE or values of the part with column weight of 1 are calculated by usinga formula. To be specific, only first 17 columns or first 14 columns inthe original complete matrix are stored. Because the part C is an allzero matrix and can be obtained, and the part E is an identity matrix,for a location of a non-zero-element in the part E, a correspondingcolumn index may be obtained through calculation based on a number of acurrently processed row. For example, when the currently processed rowis row 18, a non-zero-element corresponding to the part E is located incolumn 28; when the currently processed row is row 19, anon-zero-element corresponding to the part E is located in column 29;and so on. If locations of all non-zero-elements in the part E areobtained through calculation, a calculation result may be stored or maynot be stored. A location of a non-zero-element can be obtained when thecorresponding row and column are calculated in the encoding or decodingprocess

In another implementation, the first 14 columns in the original completematrix are stored. In a part that is not stored on the right side of thematrix, a location of a non-zero-element in the part that is not storedmay be obtained through calculation. For example, when a currentlyprocessed row is row 4, a non-zero-element corresponding to a storedpart is located in column 14; when a currently processed row is row 5, anon-zero-element corresponding to a stored part is located in column 15;and so on. When locations of all non-zero-elements in the part that isnot stored in the matrix are obtained through calculation, a calculationresult may be stored or may not be stored. A location of anon-zero-element can be obtained when the corresponding row and columnare calculated in the encoding or decoding process

In another implementation, first 14+x columns in the original completematrix are stored. In an unstored part of the right side of the matrix,first 4 rows are an all zero matrix, the other part is an identitymatrix, and a location of a non-zero-element in the part that is notstored may be obtained through calculation. For example, when acurrently processed row is row 3+x, a non-zero-element corresponding tothe part that is not stored is located in column (14+x)z; when acurrently processed row is row (3+x)+1, a non-zero-element correspondingto the part E is located in column (14+x)z+1; and so on. When locationsof all non-zero-elements in the part that is not stored in the matrixare obtained through calculation, a calculation result may be stored.Alternatively, a calculation result may not be stored and a location ofa non-zero-element can be calculated when encoding or decoding acorresponding row and column.

In still another implementation, when a shift matrix is being stored,values recorded in the shift matrix may be stored, or a value obtainedafter simple mathematical transformation is performed on values in theshift matrix described in this application may be stored.

In an implementation, the values in the shift matrix are transformed andthen stored. During transformation, transformation is performed row byrow starting from the first row in a current shift matrix. In case of anelement (for example, −1) representing an all zero matrix, the elementis stored without transformation. In case of an element (a nonnegativeelement) that represents a non-zero matrix and that is the first element(a nonnegative element) representing the non-zero matrix in the column,the element is stored without transformation. In case of an element (anonnegative element) that represents a non-zero-element matrix and thatis not the first element (a nonnegative element) representing thenon-zero matrix in the column, a difference between the nonnegativeelement and a previous element representing the non-zero matrix in thesame column is stored. If the difference is positive, it indicates rightshifting. If the difference is negative, it indicates left shifting.

It should be noted that similar transformation may not be performedstarting from the first row in the shift matrix, and may be performedstarting from any row. After similar transformation is performed on thelast row in the matrix, transformation continues to be performedstarting from the first row. In addition, such a difference storagemanner may vary based on different lifting factors Z. An actual shiftvalue be calculated according to P_(i,j)=mod(V_(i,j), Z_(c)), and then adifference is calculated.

In an encoding/decoding process, a shift value before transformation maybe restored through recursion calculation based on a value of a previouselement in a same column. Alternatively, a relative shift value may beused to perform encoding and decoding.

In an implementation, the value V_(i,j) in the shift matrix may betransformed and then stored. In a transformation operation process,locations and values of all elements (for example, −1) representing anall zero matrix in the matrix remain unchanged. For an element (anonnegative element) representing a non-zero matrix, assuming that anoriginal value of the element is V_(i,j), the transformed value is(z−V_(i,j)) mod z. In an actual encoding/decoding process, a leftshifting operation (which is originally a right shifting operation) isperformed on an identity matrix based on the transformed shift value, soas to implement normal encoding and decoding.

In an implementation, the value V_(i,j) in the shift value matrix istransformed and then stored. In a transformation operation process, anoriginal decimal shift value is transformed into a number in anotherbase, such as a binary system, an octal system, or a hexadecimal system.In an encoding/decoding process, a transformed shift value matrix may bechosen for restoration, and then is encoded/decoded. Alternatively, atransformed shift value matrix may be directly used forencoding/decoding.

In an implementation, an encoder side does not store a check matrix, butstores a possibly required generation matrix for encoding. It is assumedthat a to-be-encoded bit segment is c={c₀, c₁, c₂, c₃, . . . , c_(K−1)},and an encoded bit segment is d={d₀, d₁, . . . , d_(N−1)}. Thegeneration matrix G satisfies d=c·G.

The generation matrix may be obtained by transforming the matrix H. Aright side of the matrix H may be transformed into a form of a diagonalmatrix through row/column transformation, and may be represented as:

H=[PI]  (2)

In this case, the corresponding generation matrix G satisfies:

G=[IP ^(T)]  (3)

The check matrix H may be any one of the parity matrices or basematrices in the foregoing embodiments, or the LDPC matrix. Duringencoding, the encoded bit segment d={d₀, d₁, d₂, . . . d_(N−1)} may becalculated based on the to-be-encoded bit segment c={c₀, c₁, c₂, c₃, . .. , c_(K−1)} by using the stored generation matrix G.

In an implementation, during encoding, for a dual diagonal part of thematrix, encoding may be performed in any one of the foregoing manners orby using a method for storing a matrix having a plurality ofsuperimposed rows.

In an implementation, a shift matrix corresponding to each liftingfactor Z may be calculated based on P_(i,j)=mod(V_(i,j), Z_(c)), andthen, matrices corresponding to 51 lifting factors are all stored forencoding/decoding.

Optionally, in a communication system, encoding may be performed byusing the foregoing method, to obtain the LDPC code. After the LDPC codeis obtained, the communication apparatus may further perform thefollowing one or more operations: performing rate matching on the LDPCcode; interleaving, according to an interleaving solution, the LDPC codeon which rate matching is performed; modulating the interleaved LDPCcode according to a modulation scheme, to obtain a bit sequence X; andsending the bit sequence X.

Decoding is a reverse process of encoding. A base matrix used duringdecoding and a base matrix used during encoding have samecharacteristics. For an encoding process of the LDPC code, reference maybe made to the descriptions in the foregoing implementations. Detailsare not described herein again. In an implementation, before decoding,the communication apparatus may further perform the following one ormore operations: receiving a signal including information that is basedon LDPC encoding, demodulating the signal, performing deinterleaving andrate de-matching to obtain a soft value sequence of the LDPC code, anddecoding the soft value sequence of the LDPC code. Alternatively,decoding may be performed based on a complete base graph, a completebase graph that includes no built-in puncture column, or some rows andcolumns of a complete base graph.

The “storage” in this application may be storage in one or morememories. The one or more memories may be separately disposed, or may beintegrated into an encoder, a decoder, a processor, a chip, acommunication apparatus, or a terminal. Alternatively, some of the oneor more memories may be separately disposed, or may be integrated into adecoder, a processor, a chip, a communication apparatus, or a terminal.The memory may be a storage medium in any form. This is not limited inthis application.

Corresponding to the designs of the data processing process described inFIG. 5 and FIG. 6, an embodiment of the present application furtherprovides a corresponding communication apparatus. The communicationapparatus includes a corresponding module configured to perform eachpart in FIG. 5 or FIG. 6. The module may be software, hardware, or acombination of software and hardware. For example, the module mayinclude a memory, an electronic device, an electronic component, a logiccircuit, or any combination thereof. FIG. 7 is a schematic structuraldiagram of a communication apparatus 700. The apparatus 700 may beconfigured to implement the methods described in the foregoing methodembodiments. For details, reference may be made to the descriptions inthe foregoing method embodiments. The communication apparatus 700 may bea chip, a base station, a terminal, or another network device.

The communication apparatus 700 includes one or more processors 701. Theprocessor 701 may be a general-purpose processor or a dedicatedprocessor, for example, a baseband processor or a central processingunit. The baseband processor may be configured to process acommunication protocol and communication data. The central processingunit may be configured to control the communication apparatus (forexample, a base station, a terminal, or a chip) to execute a softwareprogram, and process data in the software program.

In a possible design, one or more modules in FIG. 5 and FIG. 6 may beimplemented by one or more processors, or by one or more processors andmemories.

In a possible design, the communication apparatus 700 includes one ormore processors 701. The one or more processors 701 can implement theencoding/decoding function. For example, the communication apparatus maybe an encoder or a decoder. In another possible design, the processor701 can implement other functions in addition to the encoding/decodingfunction.

The communication apparatus 700 encodes/decodes an input sequence basedon an LDPC matrix. A base matrix of the LDPC matrix may be any basematrix in the foregoing examples, a base matrix obtained by performingtransformation on a row order, a column order, or a row order and acolumn order in any base matrix listed above, a base matrix obtained byshortening or puncturing based on any base matrix listed above, or amatrix obtained through spreading of any base matrix listed above. Forencoding/decoding processing, reference may be made to the descriptionsof related parts in FIG. 5 and FIG. 6. Details are not described hereinagain.

Optionally, in a design, the processor 701 may include an instruction703 (or sometimes referred to as code or a program). The instruction mayrun in the processor, so that the communication apparatus 700 performsthe methods described in the foregoing embodiments. In another possibledesign, the communication apparatus 700 may further include a circuit.The circuit can implement the encoding/decoding function in theforegoing embodiments.

Optionally, in a design, the communication apparatus 700 may include oneor more memories 702. The memory 702 stores an instruction 704. Theinstruction may run in the processor, so that the communicationapparatus 700 performs the methods described in the foregoing methodembodiments.

Optionally, the memory may further store data. Optionally, the processormay further store an instruction and/or data. The processor and thememory may be disposed separately or may be integrated together.

Optionally, the “storage” in the foregoing embodiments may be storage inthe memory 702, or may be storage in another external memory or astorage device.

For example, the one or more memories 702 may store a parameter relatedto the LDPC matrix listed above, for example, a parameter related to abase matrix, such as a shift value, a base graph, spreading of a matrixbased on a base graph, each row in a base matrix, a lifting factor, abase matrix, or spreading of a matrix based on a base matrix. Fordetails, reference may be made to the related descriptions in the partin FIG. 5.

Optionally, the communication apparatus 700 may further include atransceiver 705 and an antenna 706. The processor 701 may be referred toas a processing unit, and controls the communication apparatus (aterminal or a base station). The transceiver 505 may be referred to as atransceiver unit, a transceiver circuit, or the like, and is configuredto implement sending and receiving functions of the communicationapparatus 700 by using the antenna 506.

Optionally, the communication apparatus 700 may further include a devicefor transport block CRC generation, a device for code block segmentationand a CRC check, an interleaver for interleaving, a device for ratematching, a modulator for modulation processing, or the like. Functionsof these devices may be implemented by using the one or more processors701.

Optionally, the communication apparatus 700 may further include ademodulator for a demodulation operation, a deinterleaver fordeinterleaving, a device for rate de-matching, a device for code blockconcatenation and a CRC check, or the like. Functions of these devicesmay be implemented by using the one or more processors 701.

FIG. 8 is a schematic diagram of a communication system 800. Thecommunication system 800 includes communication devices 80 and 81.Information data is received and sent between the communication devices80 and 81. The communication devices 80 and 81 may be the communicationapparatus 700, or the communication devices 80 and 81 each include thecommunication apparatus 700, and receive and/or send the informationdata. In an example, the communication device 80 may be a terminal, andthe corresponding communication device 81 may be a base station. Inanother example, the communication device 80 may be a base station, andthe corresponding communication device 81 may be a terminal.

It is further understood that various illustrative logical blocks andsteps may be implemented by electronic hardware, computer software, or acombination thereof. Whether such functions are implemented by hardwareor software depends on a particular application and a design requirementof an entire system. For each particular application, various methodsmay be used to implement the functions. However, such implementationsshould not be construed as going beyond the protection scope of theembodiments of the present application.

The technologies described in this application can be implemented invarious manners. For example, the technologies may be implemented byhardware, software, or a combination thereof. For implementation byhardware, a processing unit configured to implement the technologies inthe communication apparatus (for example, a base station, a terminal, anetwork entity, or a chip) can be implemented in one or moregeneral-purpose processors, a digital signal processor (DSP), a digitalsignal processing device (DSPD), an application-specific integratedcircuit (ASIC), a programmable logic device (PLD), a field programmablegate array (FPGA), another programmable logic apparatus, a discretegate, a transistor logic, a discrete hardware component, or anycombination thereof. The general-purpose processor may be amicroprocessor. Optionally, the general-purpose processor may be anyconventional processor, controller, microcontroller, or status machine.The processor may be implemented by using a combination of computingapparatuses, for example, a digital signal processor and amicroprocessor, a plurality of microprocessors, one or moremicroprocessors in combination with a digital signal processor core, orany other similar configurations.

The steps of the methods or the algorithms described in the embodimentsof the present application may be directly embedded into hardware, aninstruction executed by a processor, or a combination thereof. Thememory may be a RAM memory, a flash memory, a ROM memory, an EPROMmemory, an EEPROM memory, a register, a hard disk, a removable disk, aCD-ROM, or any other form of storage medium in the art. For example, thememory may be connected to the processor, so that the processor can readinformation from the memory, and store and write information in thememory. Optionally, the memory may be integrated into the processor. Theprocessor and the memory may be disposed in the ASIC, and the ASIC maybe disposed in a terminal or a base station or other network devices.Optionally, the processor and the memory may be disposed in differentcomponents of the terminal or a base station or other network devices.

With descriptions of the foregoing implementations, the presentapplication may be implemented by hardware, firmware, or a combinationthereof. When the embodiments of the present application is implementedby a software program, the implementation may be fully or partially in aform of a computer program product, where the computer program productincludes one or more computer instructions. When the computerinstructions are loaded and executed, the procedures or functionsaccording to the embodiments of the present application are all orpartially generated. When the present application is implemented by thesoftware program, the foregoing functions may alternatively be stored ina computer-readable medium or transmitted as one or more instructions orcode in the computer-readable medium. The computer may be ageneral-purpose computer, a dedicated computer, a computer network, oranother programmable apparatus. The computer-readable medium includes acomputer storage medium and a communication medium, where thecommunication medium includes any medium that enables a computer programto be transmitted from one place to another. The storage medium may beany available medium that can be accessed by a computer. The computerreadable medium may be the memory as described above. For example, ifsoftware is transmitted from a website, a server, or another remotesource by using a coaxial cable, an optical fiber/cable, a twisted pair,a digital subscriber line (DSL), or wireless technologies such asinfrared ray, radio, and microwave, the coaxial cable, opticalfiber/cable, twisted pair, DSL, or wireless technologies such asinfrared ray, radio, and microwave are included in definitions ofmediums to which they belong. For example, a disk and a disc used by thepresent application include a compact disc (CD), a laser disc, anoptical disc, a digital versatile disc (DVD), a floppy disk, and aBlu-ray disc, where the disk generally copies data magnetically, and thedisc copies data optically by using a laser. The foregoing combinationshould also be included in the protection scope of the computer-readablemedium.

It should be noted that “/” in this application represents and/or. Forexample, “encoding/decoding (encoding and/or decoding)” means encoding,decoding, or encoding and decoding.

In conclusion, what is described above is merely examples of embodimentsof the technical solutions of the present application, but is notintended to limit the protection scope of the present application. Anymodification, equivalent replacement, or improvement made withoutdeparting from principle of the present application shall fall withinthe protection scope of the present application.

What is claimed is:
 1. A method for wireless communication, comprising:obtaining, by a communication apparatus, an input sequence c, whereinthe input sequence comprises K bits, K≥1; encoding, by the communicationapparatus, the input sequence c using a matrix H, to obtain an encodedsequence d, wherein the encoded sequence d comprises N bits, and N is apositive integer; and outputting, by the communication apparatus, theencoded sequence d; wherein the matrix H is determined according to abase matrix and a lifting factor Z, Z is a positive integer; wherein thebase matrix comprises m rows and n columns, and elements in the basematrix are respectively represented by their row index i and columnindex j, where 0≤i<m, 0≤j<n; wherein an element in the base matrix iseither a zero-element or a non-zero-element, and a non-zero-element atrow i and column j has a value V_(i,j); wherein each zero element in thebase matrix corresponds to an all-zero matrix of size Z×Z in the matrixH, and a non-zero-element in row i and column j in the base matrixcorresponds to a circular permutation matrix h_(i,j) of size Z×Z in thematrix H; wherein the circular permutation matrix h_(i,j) equals to aZ×Z identity matrix been circularly shifted to the right for P_(i,j)times, where P_(i,j)=mod(V_(i,j), Z); and wherein the base matrixcomprises the following non-zero elements whose row indexes (i), columnindexes (j) and corresponding values V_(i,j) are as follows: i jV_(i, j) 0 0 0 1 0 2 0 3 0 6 0 9 0 10 0 11 0 1 0 137 3 124 4 0 5 0 6 887 0 8 0 9 55 11 0 12 0 2 0 20 1 94 3 99 4 9 8 108 10 1 12 0 13 0 3 1 382 15 4 102 5 146 6 12 7 57 8 53 9 46 10 0 13 0


2. The method according to claim 1, wherein N is equal to 50×Z.
 3. Themethod according to claim 1, wherein the input sequence c is representedas c={c₀, c₁, c₂, . . . , c_(k−1)}, and the encoded sequence d isrepresented as d={d₀, d₁, d₂, . . . , d_(N−1)}, wherein in encoding theinput sequence c using the matrix H, an element c_(k) (k=0, 1, 2, . . ., K−1) in the input sequence c and an element do (n=0, 1, 2, . . . ,N−1) in the encoded sequence d satisfy: for k=2Z to K−1, if c_(k) is nota filling bit, d_(k−2z)=c_(k); and if c_(k) is a filling bit, c_(k)=0,and d_(k−2Z) is a filling bit.
 4. The method according to claim 1,wherein the input sequence c is represented as c={c₀, c₁, c₂, . . . ,c_(k−1)}, and the encoded sequence d is represented as d={d₀, d₁, d₂, .. . , d_(N−1)}, wherein the encoded sequence d comprises K₀ bits fromthe input sequence c and N−K₀ parity bits from a parity sequence w, theparity sequence w is represented as w={w₀, w₁, w₂, . . . , w_(N−K0−1)},wherein K₀ is an integer and 0<K₀≤K; wherein the matrix H, the paritysequence w and the input sequence c satisfy: ${{H \times \begin{bmatrix}c \\w\end{bmatrix}} = 0},$ wherein c=[c₀, c₁, c₂, . . . , c_(K−1)]^(T),w=[w₀, w₁, w₂, . . . , w_(n−K0−1)]^(T), and 0 is a column vector inwhich all elements are equal to zero.
 5. The method according to claim4, wherein the parity sequence w has N+2Z−K bits and the parity sequencew is represented as w={w₀, w₁, w₂, . . . , w_(N+2Z−K−1)}.
 6. The methodaccording to claim 5, wherein in encoding the input sequence c using thematrix H, an element in the parity sequence w and an element in theencoded sequence d satisfy: for k=K to N+2Z−1, d_(k−2z)=w_(k−K).
 7. Themethod according to claim 1, wherein Z is a minimum value that satisfiesK_(b)×Z≥K, and K_(b) is one of {6, 8, 9, 10}.
 8. The method according toclaim 7, wherein K_(b) satisfies: $K_{b} = \left\{ \begin{matrix}{10,} & {K > 640} \\{9,} & {560 < K \leq 640} \\{8,} & {192 < K \leq 560} \\{6,} & {others}\end{matrix} \right.$
 9. The method according to claim 1, wherein Z isone of 5, 10, 20, 40, 80, 160 and
 320. 10. The method according to claim1, wherein m≤42 and n≤52.
 11. The method according to claim 1, whereinthe base matrix further comprises one or more rows withnon-zero-elements, wherein row indexes (i), column indexes (j) andcorresponding values V_(i,j) of the non-zero-elements are as follows: ij V_(i, j) 4 0 0 1 136 11 157 14 0 5 0 0 1 131 5 142 7 141 11 64 15 0 60 0 5 124 7 99 9 45 11 148 16 0 7 1 0 5 45 7 148 11 96 13 78 17 0 8 0 01 65 12 87 18 0 9 1 0 8 97 10 51 11 85 19 0 10 0 0 1 17 6 156 7 20 20 011 0 0 7 7 9 4 13 2 21 0 12 1 0 3 113 11 48 22 0 13 0 0 1 112 8 102 1326 23 0 14 1 0 6 138 11 57 13 27 24 0 15 0 0 10 73 11 99 25 0 16 1 0 979 11 111 12 143 26 0 17 1 0 5 24 11 109 12 18 27 0 18 0 0 6 18 7 86 280 19 0 0 1 158 10 154 29 0 20 1 0 4 148 11 104 30 0 21 0 0 8 17 13 33 310 22 1 0 2 4 32 0 23 0 0 3 75 5 158 33 0 24 1 0 2 69 9 87 34 0 25 0 0 565 35 0 26 2 0 7 100 12 13 13 7 36 0 27 0 0 6 32 37 0 28 1 0 2 126 5 11038 0 29 0 0 4 154 39 0 30 2 0 5 35 7 51 9 134 40 0 31 1 0 13 20 41 0 320 0 5 20 12 122 42 0 33 2 0 7 88 10 13 43 0 34 0 0 12 19 13 78 44 0 35 10 5 157 11 6 45 0 36 0 0 2 63 7 82 46 0 37 10 0 13 144 47 0 38 1 0 5 9311 19 48 0 39 0 0 7 24 12 138 49 0 40 2 0 10 36 13 143 50 0 41 1 0 5 211 55 51 0


12. An apparatus for wireless communication, comprising at least oneprocessor configured to: obtain an input sequence c, wherein the inputsequence comprises K bits, K≥1; encode the input sequence c using amatrix H, to obtain an encoded sequence d, wherein the encoded sequenced comprises N bits, and N is a positive integer; and output the encodedsequence d; wherein the matrix H is determined according to a basematrix and a lifting factor Z, Z is a positive integer; wherein the basematrix comprises m rows and n columns, and elements in the base matrixare respectively represented by their row index i and column index j,where 0≤i<m, 0≤j<n; wherein an element in the base matrix is either azero-element or a non-zero element, and a non-zero-element at row i andcolumn j has a value V_(i,j); wherein each zero element in the basematrix corresponds to an all-zero matrix of size Z×Z in the matrix H,and a non-zero-element in row i and column j in the base matrixcorresponds to a circular permutation matrix h_(i,j) of size Z×Z in thematrix H; wherein the circular permutation matrix h_(i,j) equals to aZ×Z identity matrix been circularly shifted to the right for P_(i,j)times, where P_(i,j)=mod(V_(i,j), Z); and wherein the base matrixcomprises the following non-zero elements whose row indexes (i), columnindexes (j) and corresponding values V_(i,j) are as follows: i jV_(i, j) 0 0 0 1 0 2 0 3 0 6 0 9 0 10 0 11 0 1 0 137 3 124 4 0 5 0 6 887 0 8 0 9 55 11 0 12 0 2 0 20 1 94 3 99 4 9 8 108 10 1 12 0 13 0 3 1 382 15 4 102 5 146 6 12 7 57 8 53 9 46 10 0 13 0


13. The apparatus according to claim 12, wherein N is equal to 50×Z. 14.The apparatus according to claim 12, wherein the input sequence c isrepresented as c={c₀, c₁, c₂, . . . , c_(k−1)}, and the encoded sequenced is represented as d={d₀, d₁, d₂, . . . , d_(N−1)}, wherein in encodingthe input sequence c using the matrix H, an element c_(k) (k=0, 1, 2, .. . , K−1) in the input sequence c and an element do (n=0, 1, 2, . . . ,N−1) in the encoded sequence d satisfy: for k=2Z to K−1, if c_(k) is nota filling bit, d_(k−2z)=c_(k); and if c_(k) is a filling bit, c_(k)=0,and d_(k−2Z) is a filling bit.
 15. The apparatus according to claim 12,wherein the input sequence c is represented as c={c₀, c₁, c₂, . . . ,c_(k−1)}, and the encoded sequence d is represented as d={d₀, d₁, d₂, .. . , d_(N−1)}, wherein the encoded sequence d comprises K₀ bits fromthe input sequence c and N−K₀ parity bits from a parity sequence w, theparity sequence w is represented as w={w₀, w₁, w₂, . . . , w_(N−K0−1)},wherein K₀ is an integer and 0<K₀≤K; wherein the matrix H, the paritysequence w and the input sequence c satisfy: ${{H \times \begin{bmatrix}c \\w\end{bmatrix}} = 0},$ wherein c=[c₀, c₁, c₂, . . . , c_(K−1)]^(T),w=[w₀, w₁, w₂, . . . , w_(n−K0−1)]^(T), and 0 is a column vector inwhich all elements are equal to zero.
 16. The apparatus according toclaim 15, wherein the parity sequence w has N+2Z−K bits and the paritysequence w is represented as w={w₀, w₁, w₂, . . . , w_(N+2Z−K−1)}. 17.The apparatus according to claim 16, wherein in encoding the inputsequence c using the matrix H, an element in the parity sequence w andan element in the encoded sequence d and satisfy: for k=K to N+2Z−1,d_(k−2z)=w_(k−K).
 18. The apparatus according to claim 12, wherein Z isa minimum value that satisfies K_(b)×Z≥K, and K_(b) is one of {6, 8, 9,10}.
 19. The apparatus according to claim 18, wherein K_(b) satisfies:$K_{b} = \left\{ \begin{matrix}{10,} & {K > 640} \\{9,} & {560 < K \leq 640} \\{8,} & {192 < K \leq 560} \\{6,} & {others}\end{matrix} \right.$
 20. The apparatus according to claim 12, wherein Zis one of 5, 10, 20, 40, 80, 160, and
 320. 21. The apparatus accordingto claim 12, wherein m≤42 and n≤52.
 22. The apparatus according to claim12, wherein the base matrix further comprises one or more rows withnon-zero-elements, wherein row indexes (i), column indexes (j) andcorresponding values V_(i,j) of the non-zero-elements are as follows: ij V_(i, j) 4 0 0 1 136 11 157 14 0 5 0 0 1 131 5 142 7 141 11 64 15 0 60 0 5 124 7 99 9 45 11 148 16 0 7 1 0 5 45 7 148 11 96 13 78 17 0 8 0 01 65 12 87 18 0 9 1 0 8 97 10 51 11 85 19 0 10 0 0 1 17 6 156 7 20 20 011 0 0 7 7 9 4 13 2 21 0 12 1 0 3 113 11 48 22 0 13 0 0 1 112 8 102 1326 23 0 14 1 0 6 138 11 57 13 27 24 0 15 0 0 10 73 11 99 25 0 16 1 0 979 11 111 12 143 26 0 17 1 0 5 24 11 109 12 18 27 0 18 0 0 6 18 7 86 280 19 0 0 1 158 10 154 29 0 20 1 0 4 148 11 104 30 0 21 0 0 8 17 13 33 310 22 1 0 2 4 32 0 23 0 0 3 75 5 158 33 0 24 1 0 2 69 9 87 34 0 25 0 0 565 35 0 26 2 0 7 100 12 13 13 7 36 0 27 0 0 6 32 37 0 28 1 0 2 126 5 11038 0 29 0 0 4 154 39 0 30 2 0 5 35 7 51 9 134 40 0 31 1 0 13 20 41 0 320 0 5 20 12 122 42 0 33 2 0 7 88 10 13 43 0 34 0 0 12 19 13 78 44 0 35 10 5 157 11 6 45 0 36 0 0 2 63 7 82 46 0 37 10 0 13 144 47 0 38 1 0 5 9311 19 48 0 39 0 0 7 24 12 138 49 0 40 2 0 10 36 13 143 50 0 41 1 0 5 211 55 51 0


23. The apparatus according to claim 12, further comprising at least onememory configured to store the base matrix, one or more lifting factorsZ, or one or more circular permutation matrices.
 24. The apparatusaccording to claim 12, further comprising at least one memory configuredto store parameters associate with the matrix H.
 25. The apparatusaccording to claim 12, further comprising a transceiver configured to:receive the input sequence and transmit the encoded sequence d.
 26. Anon-transitory computer-readable storage medium, storing instructions,which, when executed by a computer, cause the computer to perform aprocess that comprises: obtain an input sequence c, wherein the inputsequence comprises K bits, K≥1; encode the input sequence c using amatrix H, to obtain an encoded sequence d, wherein the encoded sequenced comprises N bits, and N is a positive integer; and output the encodedsequence d; wherein the matrix H is determined according to a basematrix and a lifting factor Z; wherein the base matrix comprises m rowsand n columns, and elements in the base matrix are respectivelyrepresented by their row index i and column index j, where 0≤i<m, 0≤j<n;wherein an element in the base matrix is either a zero-element or anon-zero element, and a non-zero-element at row i and column j has avalue V_(i,j); wherein each zero element in the base matrix correspondsto an all-zero matrix of size Z×Z in the matrix H, and anon-zero-element in row i and column j in the base matrix corresponds toa circular permutation matrix h_(i,j) of size Z×Z in the matrix H;wherein the circular permutation matrix h_(i,j) equals to a Z×Z identitymatrix been circularly shifted to the right for P_(i,j) times, whereP_(i,j)=mod(V_(i,j), Z); and wherein the base matrix comprises thefollowing non-zero elements whose row indexes (i), column indexes (j)and corresponding values V_(i,j) are as follows: i j V_(i, j) 0 0 0 1 02 0 3 0 6 0 9 0 10 0 11 0 1 0 137 3 124 4 0 5 0 6 88 7 0 8 0 9 55 11 012 0 2 0 20 1 94 3 99 4 9 8 108 10 1 12 0 13 0 3 1 38 2 15 4 102 5 146 612 7 57 8 53 9 46 10 0 13 0


27. The non-transitory computer-readable storage medium according toclaim 26, wherein the input sequence c is represented as c={c₀, c₁, c₂,. . . , c_(k−1)}, and the encoded sequence d is represented as d={d₀,d₁, d₂, . . . , d_(N−1)}, an element c_(k) (k=0, 1, 2, . . . , K−1) inthe input sequence c and an element do (n=0, 1, 2, . . . , N−1) in theencoded sequence d satisfy: for k=2Z to K−1, if c_(k) is not a fillingbit, d_(k−2z)=c_(k); and if c_(k) is a filling bit, c_(k)=0, andd_(k−2Z) is a filling bit.
 28. The non-transitory computer-readablestorage medium according to claim 26, wherein the input sequence c isrepresented as c={c₀, c₁, c₂, . . . , c_(k−1)}, and the encoded sequenced is represented as d={d₀, d₁, d₂, . . . , d_(N−1)}, wherein the encodedsequence d comprises K₀ bits from the input sequence c and N−K₀ paritybits from a parity sequence w, the parity sequence w is represented asw={w₀, w₁, w₂, . . . , w_(N−K0−1)}, wherein K₀ is an integer and 0<K₀≤K;wherein the matrix H, the parity sequence w and the input sequence csatisfy: ${{H \times \begin{bmatrix}c \\w\end{bmatrix}} = 0},$ wherein c=[c₀, c₁, c₂, . . . , c_(K−1)]^(T),w=[w₀, w₁, w₂, . . . , w_(n−K0−1)]^(T), and 0 is a column vector inwhich all elements are equal to zero.
 29. The non-transitorycomputer-readable storage medium according to claim 28, wherein theparity sequence w has N+2Z−K bits and the parity sequence w isrepresented as w={w₀, w₁, w₂, . . . w_(N+2Z−K−1)}, an element in theparity sequence w and an element in the encoded sequence d and satisfy:for k=K to N+2Z−1, d_(k−2z)=w_(k−K).
 30. The non-transitorycomputer-readable storage medium according to claim 26, wherein the basematrix further comprises one or more rows with non-zero-elements,wherein row indexes (i), column indexes (j) and corresponding valuesV_(i,j) of the non-zero-elements are as follows: i j V_(i, j) 4 0 0 1136 11 157 14 0 5 0 0 1 131 5 142 7 141 11 64 15 0 6 0 0 5 124 7 99 9 4511 148 16 0 7 1 0 5 45 7 148 11 96 13 78 17 0 8 0 0 1 65 12 87 18 0 9 10 8 97 10 51 11 85 19 0 10 0 0 1 17 6 156 7 20 20 0 11 0 0 7 7 9 4 13 221 0 12 1 0 3 113 11 48 22 0 13 0 0 1 112 8 102 13 26 23 0 14 1 0 6 13811 57 13 27 24 0 15 0 0 10 73 11 99 25 0 16 1 0 9 79 11 111 12 143 26 017 1 0 5 24 11 109 12 18 27 0 18 0 0 6 18 7 86 28 0 19 0 0 1 158 10 15429 0 20 1 0 4 148 11 104 30 0 21 0 0 8 17 13 33 31 0 22 1 0 2 4 32 0 230 0 3 75 5 158 33 0 24 1 0 2 69 9 87 34 0 25 0 0 5 65 35 0 26 2 0 7 10012 13 13 7 36 0 27 0 0 6 32 37 0 28 1 0 2 126 5 110 38 0 29 0 0 4 154 390 30 2 0 5 35 7 51 9 134 40 0 31 1 0 13 20 41 0 32 0 0 5 20 12 122 42 033 2 0 7 88 10 13 43 0 34 0 0 12 19 13 78 44 0 35 1 0 5 157 11 6 45 0 360 0 2 63 7 82 46 0 37 10 0 13 144 47 0 38 1 0 5 93 11 19 48 0 39 0 0 724 12 138 49 0 40 2 0 10 36 13 143 50 0 41 1 0 5 2 11 55 51 0